Veda Skills Logical Reasoning Unit 10: Inequalities

I (V ≤ H): V ≤ H is given directly, so I is true. II (T > V): T = H ≥ V gives only T ≥ V, which does not make T > V certain (T may also be equal to V); II is not true. So only I is true.

I (V < X): V > N = X gives V > X, so V < X is false; I is not true. II (V > L): V > N = X ≥ L gives V > L, so II is true. So only II is true.

I (H < P): H < S = G ≤ P gives H < P, so I is true. II (G = S): G = S is given directly, so II is true. So both are true.

I (F > D): F ≤ C < W < D gives F < D, so F > D is false; I is not true. II (W ≥ D): W < D is given directly, so W ≥ D is false; II is not true. So neither is true.

I (K > G): K > P ≥ G gives K > G, so I is true. II (G > H): only G ≥ H is given, which does not make G > H certain (G may also be equal to H); II is not true. So only I is true.

I (X ≤ A): X > L > A gives X > A, so X ≤ A is false; I is not true. II (P < L): P ≤ A < L gives P < L, so II is true. So only II is true.

I (E = C): in E ≥ W ≤ C the signs point both ways, so E and C have no definite relation; I is not definitely true. II (W ≥ X): in W ≤ E > X the signs point both ways, so W and X have no definite relation; II is not definitely true. So neither is true.

I (U < C): U < C is given directly, so I is true. II (F > U): F > R > U gives F > U, so II is true. So both are true.

I (P > G): P ≥ D > G gives P > G, so I is true. II (R < D): in R ≥ G < D the signs point both ways, so R and D have no definite relation; II is not definitely true. So only I is true.

I (J > Q): J > Y = Q gives J > Q, so I is true. II (Q = D): in Q = Y < J ≥ T ≤ D the signs point both ways, so Q and D have no definite relation; II is not definitely true. So only I is true.

I (A > V): in A ≥ X < T ≤ V the signs point both ways, so A and V have no definite relation; I is not definitely true. II (V > X): V ≥ T > X gives V > X, so II is true. So only II is true.

I (F ≤ T): F ≤ V ≤ T gives F ≤ T, so I is true. II (Z ≥ F): Z = T ≥ V ≥ F gives Z ≥ F, so II is true. So both are true.

I (P > T): in P ≤ D > V = T the signs point both ways, so P and T have no definite relation; I is not definitely true. II (X = V): X > T = V gives X > V, so X = V is false; II is not true. So neither is true.

I (N ≤ E): in N ≤ S > E the signs point both ways, so N and E have no definite relation; I is not definitely true. II (N > E): in N ≤ S > E the signs point both ways, so N and E have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (V > D): in V ≤ E = Y ≥ D the signs point both ways, so V and D have no definite relation; I is not definitely true. II (V ≤ Y): V ≤ E = Y gives V ≤ Y, so II is true. So only II is true.

I (L ≤ U): L ≤ R = U gives L ≤ U, so I is true. II (Y ≥ L): in Y > J ≤ U = R ≥ L the signs point both ways, so Y and L have no definite relation; II is not definitely true. So only I is true.

I (M > E): in M < R > N ≥ E the signs point both ways, so M and E have no definite relation; I is not definitely true. II (M ≤ E): in M < R > N ≥ E the signs point both ways, so M and E have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (S ≥ Q): in S ≥ E ≥ P ≤ Q the signs point both ways, so S and Q have no definite relation; I is not definitely true. II (Q ≥ E): in Q ≥ P ≤ E the signs point both ways, so Q and E have no definite relation; II is not definitely true. So neither is true.

I (V > E): V > Y > E gives V > E, so I is true. II (S > E): S = C > E gives S > E, so II is true. So both are true.

I (V < D): in V ≥ G = Z ≤ D the signs point both ways, so V and D have no definite relation; I is not definitely true. II (V ≥ D): in V ≥ G = Z ≤ D the signs point both ways, so V and D have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (Z = H): Z < F ≤ H gives Z < H, so Z = H is false; I is not true. II (G ≤ H): in G ≥ A ≤ Z < F ≤ H the signs point both ways, so G and H have no definite relation; II is not definitely true. So neither is true.

I (N > C): N > K ≥ E > C gives N > C, so I is true. II (U > C): in U < V > C the signs point both ways, so U and C have no definite relation; II is not definitely true. So only I is true.

I (C > T): in C ≤ Z ≤ A ≥ T the signs point both ways, so C and T have no definite relation; I is not definitely true. II (T < E): T < S = E gives T < E, so II is true. So only II is true.

I (N ≤ C): in N < U ≥ R < C the signs point both ways, so N and C have no definite relation; I is not definitely true. II (N > C): in N < U ≥ R < C the signs point both ways, so N and C have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (T < W): T ≤ A < W gives T < W, so I is true. II (M ≤ W): M = E ≤ W gives M ≤ W, so II is true. So both are true.

I (M ≥ H): in M = B ≤ J > D ≥ H the signs point both ways, so M and H have no definite relation; I is not definitely true. II (U > H): in U ≤ M = B ≤ J > D ≥ H the signs point both ways, so U and H have no definite relation; II is not definitely true. So neither is true.

I (R < N): in R < V < H > N the signs point both ways, so R and N have no definite relation; I is not definitely true. II (R ≥ N): in R < V < H > N the signs point both ways, so R and N have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (U > C): in U > D < X < C the signs point both ways, so U and C have no definite relation; I is not definitely true. II (U = C): in U > D < X < C the signs point both ways, so U and C have no definite relation; II is not definitely true. So neither is true.

I (F < Z): in F = X ≤ B > J > Z the signs point both ways, so F and Z have no definite relation; I is not definitely true. II (F = Z): in F = X ≤ B > J > Z the signs point both ways, so F and Z have no definite relation; II is not definitely true. So neither is true.

I (C < P): C < D < P gives C < P, so I is true. II (D > T): D < P < T gives D < T, so D > T is false; II is not true. So only I is true.

I (P < K): P ≤ V < F ≤ L ≤ K gives P < K, so I is true. II (V < K): V < F ≤ L ≤ K gives V < K, so II is true. So both are true.

I (E ≥ S): in E < L > S the signs point both ways, so E and S have no definite relation; I is not definitely true. II (E < S): in E < L > S the signs point both ways, so E and S have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (D < G): in D > V < F ≤ G the signs point both ways, so D and G have no definite relation; I is not definitely true. II (D > F): in D > V < F the signs point both ways, so D and F have no definite relation; II is not definitely true. So neither is true.

I (D < L): D ≥ X ≥ L gives D ≥ L, so D < L is false; I is not true. II (X ≤ B): X ≤ D = B gives X ≤ B, so II is true. So only II is true.

I (T > B): in T < E > M < B the signs point both ways, so T and B have no definite relation; I is not definitely true. II (T ≤ B): in T < E > M < B the signs point both ways, so T and B have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (K < C): in K = F < B > C the signs point both ways, so K and C have no definite relation; I is not definitely true. II (R < C): R > B > C gives R > C, so R < C is false; II is not true. So neither is true.

I (Q ≤ H): Q ≤ P ≤ H gives Q ≤ H, so I is true. II (Q > U): in Q ≤ P ≥ M < U the signs point both ways, so Q and U have no definite relation; II is not definitely true. So only I is true.

X = D ≤ L gives X ≤ L, so X ≤ L is definitely true. X < H: the path gives X ≥ H, so it is not definite. L < H: the path gives L ≥ H, so it is not definite. D > L: the path gives D ≤ L, so it is not definite.

K < J < N gives K < N, so K < N is definitely true. J > R: J > K ≤ R has facing signs, so it is not definite. V < J: V ≤ N > J has facing signs, so it is not definite. K > V: K < J < N ≥ V has facing signs, so it is not definite.

H ≤ F < U gives H < U, so H < U is definitely true. U < J: U > F ≥ H < Q > G < J has facing signs, so it is not definite. H < G: H < Q > G has facing signs, so it is not definite. F > Q: F ≥ H < Q has facing signs, so it is not definite.

C < J ≤ G gives C < G, so C < G is definitely true. J < A: J ≤ G ≥ A has facing signs, so it is not definite. A > C: A ≤ G ≥ J > C has facing signs, so it is not definite. V < M: the path gives V = M, so it is not definite.

W ≤ M = S gives W ≤ S, so W > S is impossible. Each of the other three is possible for some order of the letters.

P < B ≤ C ≤ R gives P < R, so P ≥ R is impossible. Each of the other three is possible for some order of the letters.

With >: E > U ≥ A gives E > A. ≤ gives no definite relation; ≥ gives only E ≥ A; < gives no definite relation.

With <: S ≤ N = Z < C gives S < C. = gives only S ≤ C; ≤ gives only S ≤ C; > gives no definite relation.

With < the blank itself reads P > V. ≤ gives only P ≥ V; > gives only P < V; = gives only P = V.

With > the blank itself reads Z < R. < gives only Z > R; = gives only Z = R; ≤ gives only Z ≥ R.

With <: F > A ≥ R gives F > R. = gives only F ≥ R; ≤ gives only F ≥ R; ≥ gives no definite relation.

In V ≥ J < N < A < M: A > N > J and J < N < A < M give both relations. V ≥ J > N < A < M fails A > J (no definite relation); V ≥ J < N < A ≥ M fails J < M (no definite relation); V ≥ J ≥ N > A < M fails A > J (it gives A < J).

In M ≤ L = U ≥ E > K < W: L = U ≥ E and K < E ≤ U give both relations. M ≤ L < U ≥ E > K < W fails L ≥ E (no definite relation); M ≤ L = U ≥ E < K < W fails K < U (no definite relation); M ≤ L = U ≥ E ≤ K > W fails K < U (no definite relation).

In B ≤ P < G > Q ≥ S: S ≤ Q < G and B ≤ P < G give both relations. B ≤ P = G > Q ≥ S fails B < G (it gives B ≤ G); B ≥ P > G > Q ≥ S fails B < G (it gives B > G); B ≥ P < G > Q ≥ S fails B < G (no definite relation).

Between T and L the path T < D ≥ L has signs facing both ways, so no relation is fixed. L and B: L ≥ S = B gives L ≥ B; D and S: D ≥ L ≥ S gives D ≥ S; D and B: D ≥ L ≥ S = B gives D ≥ B.

Between Q and B the path Q ≥ A < W < G = B has signs facing both ways, so no relation is fixed. W and B: W < G = B gives W < B; A and G: A < W < G gives A < G; A and B: A < W < G = B gives A < B.

Between V and H the path V < R = N ≥ H has signs facing both ways, so no relation is fixed. N and K: N ≥ H > K gives N > K; V and N: V < R = N gives V < N; R and K: R = N ≥ H > K gives R > K.

Write each sentence with the first letters: T ≤ E, T ≥ P, T > C, M > C. I (C < E): C < T ≤ E gives C < E, so I is true. II (E = P): E ≥ T ≥ P gives only E ≥ P, which does not make E = P certain (E may also be different from P); II is not true. So only I is true.

Write each sentence with the first letters: R > H, H = G, H < O, W > G. I (G > O): G = H < O gives G < O, so G > O is false; I is not true. II (W ≤ R): in W > G = H < R the signs point both ways, so W and R have no definite relation; II is not definitely true. So neither is true.

Write each sentence with the first letters: T > O, G ≤ T, K = G, G < L. I (K ≤ T): K = G ≤ T gives K ≤ T, so I is true. II (L > K): L > G = K gives L > K, so II is true. So both are true.

Write each sentence with the first letters: W < H, W ≥ T, D < H, T = S. I (T ≥ D): in T ≤ W < H > D the signs point both ways, so T and D have no definite relation; I is not definitely true. II (T < D): in T ≤ W < H > D the signs point both ways, so T and D have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (Z > C): Z > N ≥ C gives Z > C, so I is true. II (J ≤ N): in J ≥ C ≤ N the signs point both ways, so J and N have no definite relation; II is not definitely true. So only I is true.

I (Z < B): in Z ≥ W ≤ M < H = B the signs point both ways, so Z and B have no definite relation; I is not definitely true. II (Z ≥ B): in Z ≥ W ≤ M < H = B the signs point both ways, so Z and B have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

I (N > G): only N ≥ G is given, which does not make N > G certain (N may also be equal to G); I is not true. II (K > N): in K < M ≥ N the signs point both ways, so K and N have no definite relation; II is not definitely true. So neither is true.

I (B < A): in B ≤ X > M < A the signs point both ways, so B and A have no definite relation; I is not definitely true. II (X > M): X > M is given directly, so II is true. So only II is true.

Write R > S, M ≥ S, M < K, which join as R > S ≤ M < K. I: S ≤ M < K gives K > S, true. II: R > S ≤ M has facing signs, so R and M are unknown. Only I is true.

A ≥ B rules out A < B, and B ≥ A rules out A > B. Only A = B is left.

allows only A > B. ≥ and ≤ each allow two cases.

A ≥ B ≤ C: the signs face each other at B. The others point one way.

A > B is definite. In the first pair I is true by itself, in the second II (B < A) is true by itself, and in the third both are false. Either-or needs neither to be definite.

Flip both the letters and the sign: B < A becomes A > B.

P ≥ Q > R points one way and contains >, so P > R. R is exactly the rule used.

At B the signs face each other, so A and C can be in any order. A is false; R is true.

M > N = O ≥ P has a > on a one-way path, so M > P. N = O ≥ P gives N ≥ P. Both are true.

W < X ≥ Y: signs face each other at X, so W and Y are unknown. X ≥ Y > Z gives X > Z. Only 2 is true.

Decode first (© → ≥, @ → >, & → =, % → <, # → ≤): W > J > N ≤ K; I is N < W, II is N > J. I (N < W): N < J < W gives N < W, so I is true. II (N > J): N < J is given directly, so N > J is false; II is not true. So only I is true.

Decode first (& → =, % → ≤, © → ≥, # → <, δ → >): U = Q > F ≤ J; I is J < Q, II is Q > F. I (J < Q): in J ≥ F < Q the signs point both ways, so J and Q have no definite relation; I is not definitely true. II (Q > F): Q > F is given directly, so II is true. So only II is true.

Decode first (# → ≥, ★ → >, & → <, δ → =, © → ≤): W ≤ J ≤ R > D; I is W ≤ J, II is R ≥ W. I (W ≤ J): W ≤ J is given directly, so I is true. II (R ≥ W): R ≥ J ≥ W gives R ≥ W, so II is true. So both are true.

Decode first (# → =, % → ≤, © → ≥, ★ → <, @ → >): S > F ≥ Z < L; I is F < L, II is S ≤ Z. I (F < L): in F ≥ Z < L the signs point both ways, so F and L have no definite relation; I is not definitely true. II (S ≤ Z): S > F ≥ Z gives S > Z, so S ≤ Z is false; II is not true. So neither is true.

Decode first (© → >, ★ → ≥, # → <, % → =, & → ≤): L < W ≤ D ≥ E; I is L < W, II is L > D. I (L < W): L < W is given directly, so I is true. II (L > D): L < W ≤ D gives L < D, so L > D is false; II is not true. So only I is true.

Decode first (& → >, ★ → <, δ → =, % → ≤, # → ≥): L > J ≤ Y ≥ V > X; I is L > J, II is L > V. I (L > J): L > J is given directly, so I is true. II (L > V): in L > J ≤ Y ≥ V the signs point both ways, so L and V have no definite relation; II is not definitely true. So only I is true.

Decode first (& → <, # → >, ★ → ≤, © → ≥, @ → =): J ≥ Y = G ≤ U < E; I is U < J, II is U < E. I (U < J): in U ≥ G = Y ≤ J the signs point both ways, so U and J have no definite relation; I is not definitely true. II (U < E): U < E is given directly, so II is true. So only II is true.

Decode first (% → =, ★ → ≤, & → ≥, © → >, # → <): V < B ≤ M < K > A; I is K > M, II is M > V. I (K > M): K > M is given directly, so I is true. II (M > V): M ≥ B > V gives M > V, so II is true. So both are true.

Decode first (δ → <, ★ → ≥, @ → =, © → >, % → ≤): G ≥ B = F > R ≤ S; I is G = F, II is R = S. I (G = F): G ≥ B = F gives only G ≥ F, which does not make G = F certain (G may also be different from F); I is not true. II (R = S): only R ≤ S is given, which does not make R = S certain (R may also be different from S); II is not true. So neither is true.

Decode first (% → =, @ → ≥, & → <, δ → >, # → ≤): W ≥ F ≥ Z = Q < J; I is F = Q, II is F > Q. I (F = Q): F ≥ Z = Q gives only F ≥ Q, which does not make F = Q certain (F may also be different from Q); I is not true. II (F > Q): F ≥ Z = Q gives only F ≥ Q, which does not make F > Q certain (F may also be equal to Q); II is not true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (# → ≤, © → <, @ → ≥, % → =, & → >): N < S ≥ R ≥ T = W; I is S ≥ W, II is W < T. I (S ≥ W): S ≥ R ≥ T = W gives S ≥ W, so I is true. II (W < T): W = T is given directly, so W < T is false; II is not true. So only I is true.

Decode first (& → >, ★ → <, @ → ≤, % → =, # → ≥): B ≥ Z > N > F < U; I is B < U, II is B ≥ U. I (B < U): in B ≥ Z > N > F < U the signs point both ways, so B and U have no definite relation; I is not definitely true. II (B ≥ U): in B ≥ Z > N > F < U the signs point both ways, so B and U have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (★ → ≤, & → =, # → <, δ → ≥, @ → >): L < E ≤ C > P > J; I is J < L, II is E ≥ J. I (J < L): in J < P < C ≥ E > L the signs point both ways, so J and L have no definite relation; I is not definitely true. II (E ≥ J): in E ≤ C > P > J the signs point both ways, so E and J have no definite relation; II is not definitely true. So neither is true.

Decode first (★ → <, % → ≥, # → >, δ → =, & → ≤): Y ≥ S ≥ D ≤ W < H; I is Y = H, II is H > W. I (Y = H): in Y ≥ S ≥ D ≤ W < H the signs point both ways, so Y and H have no definite relation; I is not definitely true. II (H > W): H > W is given directly, so II is true. So only II is true.

Decode first (# → >, © → =, % → <, @ → ≤, & → ≥): T ≤ E < Y ≥ F > Q; I is Q ≥ E, II is Q < E. I (Q ≥ E): in Q < F ≤ Y > E the signs point both ways, so Q and E have no definite relation; I is not definitely true. II (Q < E): in Q < F ≤ Y > E the signs point both ways, so Q and E have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (# → >, & → ≤, δ → <, % → =, @ → ≥): D ≥ W = R < V ≥ P; I is D ≥ W, II is V > W. I (D ≥ W): D ≥ W is given directly, so I is true. II (V > W): V > R = W gives V > W, so II is true. So both are true.

Decode first (@ → =, ★ → ≥, & → <, % → >, # → ≤): F ≥ E ≤ N ≤ T ≥ X = W; I is E = T, II is E < T. I (E = T): E ≤ N ≤ T gives only E ≤ T, which does not make E = T certain (E may also be different from T); I is not true. II (E < T): E ≤ N ≤ T gives only E ≤ T, which does not make E < T certain (E may also be equal to T); II is not true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (% → ≥, δ → <, # → ≤, ★ → >, @ → =): N = X ≤ H < S > Q < A; I is X > A, II is Q < H. I (X > A): in X ≤ H < S > Q < A the signs point both ways, so X and A have no definite relation; I is not definitely true. II (Q < H): in Q < S > H the signs point both ways, so Q and H have no definite relation; II is not definitely true. So neither is true.

Decode first (δ → >, ★ → ≤, # → =, © → ≥, @ → <): M = D ≤ P > B < Q < X; I is B < P, II is D > Q. I (B < P): B < P is given directly, so I is true. II (D > Q): in D ≤ P > B < Q the signs point both ways, so D and Q have no definite relation; II is not definitely true. So only I is true.

Decode first (% → =, ★ → <, & → ≥, © → ≤, # → >): A ≥ S < D ≤ L > T ≥ N; I is D < A, II is N ≤ T. I (D < A): in D > S ≤ A the signs point both ways, so D and A have no definite relation; I is not definitely true. II (N ≤ T): N ≤ T is given directly, so II is true. So only II is true.

Decode first (% → <, δ → ≥, # → ≤, @ → =, © → >): Y = E < M ≥ L ≤ H ≤ J; I is L ≤ J, II is H ≥ L. I (L ≤ J): L ≤ H ≤ J gives L ≤ J, so I is true. II (H ≥ L): H ≥ L is given directly, so II is true. So both are true.

Decode first (★ → ≥, # → =, & → >, % → <, © → ≤): L ≤ Q = H < U ≥ D < M; I is D ≤ L, II is D > L. I (D ≤ L): in D ≤ U > H = Q ≥ L the signs point both ways, so D and L have no definite relation; I is not definitely true. II (D > L): in D ≤ U > H = Q ≥ L the signs point both ways, so D and L have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (★ → ≥, © → >, @ → ≤, # → <, & → =): D < S, T > S, G < T, X ≥ G; I is D < T, II is X > D. I (D < T): D < S < T gives D < T, so I is true. II (X > D): in X ≥ G < T > S > D the signs point both ways, so X and D have no definite relation; II is not definitely true. So only I is true.

Decode first (# → ≤, % → ≥, © → <, ★ → =, & → >): W > Z, Z < N, R = Z, H < R; I is Z < H, II is R > N. I (Z < H): Z = R > H gives Z > H, so Z < H is false; I is not true. II (R > N): R = Z < N gives R < N, so R > N is false; II is not true. So neither is true.

Decode first (★ → =, % → <, © → >, δ → ≥, @ → ≤): Y < Z, Y = G, G ≥ X, C > G; I is Y > X, II is Y = X. I (Y > X): Y = G ≥ X gives only Y ≥ X, which does not make Y > X certain (Y may also be equal to X); I is not true. II (Y = X): Y = G ≥ X gives only Y ≥ X, which does not make Y = X certain (Y may also be different from X); II is not true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (© → <, @ → =, ★ → >, % → ≤, # → ≥): K ≤ Q, K ≥ X, F < Q, F = U, U ≤ W; I is W = Q, II is U < Q. I (W = Q): in W ≥ U = F < Q the signs point both ways, so W and Q have no definite relation; I is not definitely true. II (U < Q): U = F < Q gives U < Q, so II is true. So only II is true.

Decode first (© → <, & → >, δ → ≥, % → ≤, # → =): L > R, R < X, L < Q, Q ≤ Z, Z < D; I is X > D, II is X ≤ D. I (X > D): in X > R < L < Q ≤ Z < D the signs point both ways, so X and D have no definite relation; I is not definitely true. II (X ≤ D): in X > R < L < Q ≤ Z < D the signs point both ways, so X and D have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (& → >, ★ → ≥, @ → <, δ → =, % → ≤): F > K, L ≤ K, H < L, U ≤ H, A < H; I is H = F, II is K < A. I (H = F): H < L ≤ K < F gives H < F, so H = F is false; I is not true. II (K < A): K ≥ L > H > A gives K > A, so K < A is false; II is not true. So neither is true.

Decode first (& → <, © → ≥, δ → ≤, # → =, % → >): T ≤ F, T > H, T < M, H ≥ G, V < G; I is H < F, II is T > V. I (H < F): H < T ≤ F gives H < F, so I is true. II (T > V): T > H ≥ G > V gives T > V, so II is true. So both are true.

Replace each symbol by its sign (δ → >, © → ≥, ★ → <, @ → =, # → ≤): Z ★ A δ N ★ Y becomes Z < A > N < Y.

Replace each symbol by its sign (© → <, @ → ≥, # → ≤, & → =, ★ → >): Z ★ A ★ R & K © W becomes Z > A > R = K < W.

Replace each symbol by its sign (★ → >, δ → ≤, & → ≥, @ → =, © → <): P © C δ J ★ K δ Z becomes P < C ≤ J > K ≤ Z.

Replace each symbol by its sign (# → >, % → <, @ → ≤, & → =, δ → ≥): N & E @ R δ S @ C @ A becomes N = E ≤ R ≥ S ≤ C ≤ A.

Replace each symbol by its sign (& → =, % → >, @ → ≥, δ → <, © → ≤): N @ P % F % V © L & T becomes N ≥ P > F > V ≤ L = T.

Write each sign as its symbol (< → @, ≥ → &, > → ©, ≤ → %, = → #): R ≤ Q ≥ N = V becomes R % Q & N # V. Each other option has one wrong symbol.

Write each sign as its symbol (= → @, > → ★, < → #, ≥ → &, ≤ → δ): U < P < T > Y ≤ C becomes U # P # T ★ Y δ C. Each other option has one wrong symbol.

Write each sign as its symbol (> → &, ≥ → ©, = → %, ≤ → δ, < → #): D = M < H ≥ N ≥ K ≤ X becomes D % M # H © N © K δ X. Each other option has one wrong symbol.

Write each sign as its symbol (≥ → &, ≤ → @, = → %, < → ©, > → #): B < M < P ≤ F > Z becomes B © M © P @ F # Z. Each other option has one wrong symbol.

Change every sign to its real meaning: Y ≤ H > J > V; I is V < H, II is Y > V. I (V < H): V < J < H gives V < H, so I is true. II (Y > V): in Y ≤ H > J > V the signs point both ways, so Y and V have no definite relation; II is not definitely true. So only I is true.

Change every sign to its real meaning: R ≤ S ≤ Q < M ≥ N; I is R = M, II is R < S. I (R = M): R ≤ S ≤ Q < M gives R < M, so R = M is false; I is not true. II (R < S): only R ≤ S is given, which does not make R < S certain (R may also be equal to S); II is not true. So neither is true.

Change every sign to its real meaning: X ≥ L ≥ F ≤ E > J; I is L > E, II is E ≥ F. I (L > E): in L ≥ F ≤ E the signs point both ways, so L and E have no definite relation; I is not definitely true. II (E ≥ F): E ≥ F is given directly, so II is true. So only II is true.

Change every sign to its real meaning: Y ≤ G ≥ W > V ≥ X; I is Y < W, II is Y ≥ W. I (Y < W): in Y ≤ G ≥ W the signs point both ways, so Y and W have no definite relation; I is not definitely true. II (Y ≥ W): in Y ≤ G ≥ W the signs point both ways, so Y and W have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Change every sign to its real meaning: T = D > R > N ≤ J < Q; I is R > N, II is T > R. I (R > N): R > N is given directly, so I is true. II (T > R): T = D > R gives T > R, so II is true. So both are true.

Change every sign to its real meaning: V < Q > X ≤ T ≥ W; I is Q ≥ T, II is T ≥ V. I (Q ≥ T): in Q > X ≤ T the signs point both ways, so Q and T have no definite relation; I is not definitely true. II (T ≥ V): in T ≥ X < Q > V the signs point both ways, so T and V have no definite relation; II is not definitely true. So neither is true.

Decode first (# → ≤, % → =, @ → >, ★ → <, δ → ≥): D = L ≤ X > M; I is M < X, II is M ≤ D. I (M < X): M < X is given directly, so I is true. II (M ≤ D): in M < X ≥ L = D the signs point both ways, so M and D have no definite relation; II is not definitely true. So only I is true.

Decode first (# → >, @ → =, © → ≥, ★ → ≤, δ → <): Q > F ≤ L < X > N; I is Q ≤ L, II is Q > L. I (Q ≤ L): in Q > F ≤ L the signs point both ways, so Q and L have no definite relation; I is not definitely true. II (Q > L): in Q > F ≤ L the signs point both ways, so Q and L have no definite relation; II is not definitely true. Neither is definite alone, but both are about the same pair and between them they cover every case, so exactly one must hold: either I or II is true.

Decode first (% → >, ★ → ≤, & → ≥, @ → =, # → <): E ≤ L, Z < E, Z > P, G < Z; I is G = L, II is E ≤ P. I (G = L): G < Z < E ≤ L gives G < L, so G = L is false; I is not true. II (E ≤ P): E > Z > P gives E > P, so E ≤ P is false; II is not true. So neither is true.

Decode first (@ → =, δ → >, # → ≥, % → ≤, ★ → <): N > H, D ≥ N, N = R, X > R; I is X ≤ D, II is H < X. I (X ≤ D): in X > R = N ≤ D the signs point both ways, so X and D have no definite relation; I is not definitely true. II (H < X): H < N = R < X gives H < X, so II is true. So only II is true.

Not smaller leaves greater or equal: P ≥ Q.

Greater and equal are both ruled out, so only smaller is left: P < Q.

Not greater leaves smaller or equal: P ≤ Q.

Smaller and greater are ruled out; only equal is left.

Removing smaller and equal leaves only greater. "Not smaller" still allows equal; "not equal" allows smaller too.

Q # P means Q ≥ P, which is the same as P ≤ Q.

Removing "smaller" leaves greater and equal, which is ≥. R is exactly why.

Two cases are removed, so only P < Q is left; A is false. R is true.

Decoded: A ≥ B > C = D. A > D is true (one way, with >). B > C = D gives B > D, so B = D is false. Only 1.

Real statement: K ≤ L < M ≥ N. Written K = M is really K < M, and K ≤ L < M gives K < M, so 1 is true. Written L = N is really L < N, but L < M ≥ N has facing signs, so 2 is not definite.