Shared by a Veda learner · Generated with Veda AI
This exam covers key concepts in discrete structures, including relations, equivalence relations, lattices, and Hasse diagrams. Understanding the properties and operations on sets, particularly in terms of relations and…
Full explanation, worked examples & memory tricks in the app
Every question in the paper gets a full exam-length answer in the app — organised by marks, the way a topper writes it.
Define a Lattice. Draw the Hasse diagram of (D₃₆, /) and Show that it is a lattice.
A lattice is a partially ordered set where every two elements have a unique supremum and infimum; the Hasse diagram must show these relationships.
The full exam-length answer is in the app.
If A = {1, 2, 3}, B = {4, 5} and C = {1, 2, 3, 4, 5}. Find (i) A × B (ii) C × B (iii) B × B. Hence prove that: (C × B) - (A × B) = B × B.
A × B = {(1,4), (1,5), (2,4), (2,5), (3,4), (3,5)}; C × B = {(1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (4,4), (4,5), (5,4), (5,5)}; B × B = {(4,4), (4,5), (5,4), (5,5)}.
The full exam-length answer is in the app.
Identify whether the each of the following relation defined on the set A = {1, 2, 3} are reflexive relation, symmetric relation, anti-symmetric relation and transitive relation. R₁ = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 3)} R₂ = Universal Relation.
R₁ is reflexive, symmetric, and transitive; R₂ is reflexive, symmetric, anti-symmetric, and transitive.
The full exam-length answer is in the app.
Let R = {(1, 2), (2, 3), (3, 1)} and A = {1, 2, 3} find the reflexive, symmetric and transitive closure of R using composition of relation R.
The reflexive closure adds (1,1), (2,2), (3,3); the symmetric closure adds (2,1), (3,2), (1,3); the transitive closure adds (1,3), (2,1), (3,2).
The full exam-length answer is in the app.
Use Warshall's algorithm to find the transitive closure of the following relation on the set A = {1, 2, 3}. R = {(1, 2), (2, 3), (3, 1)}
Applying Warshall's algorithm yields the transitive closure R* = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}.
The full exam-length answer is in the app.
Let X = {1, 2, 3, 4, 5, 6, 7} and R = {(x, y) | (x-y) is divisible by 3}, then prove that R is an equivalence relation.
R is reflexive, symmetric, and transitive, thus proving it is an equivalence relation.
The full exam-length answer is in the app.
If R and S are equivalence relation on the set A, prove that R ∩ S is an equivalence relation.
R ∩ S is reflexive, symmetric, and transitive, hence it is an equivalence relation.
The full exam-length answer is in the app.
Define Power set. Let A = {Ø, b} construct the following set: (i) A - Ø (ii) A ∩ P(A).
The power set of A is the set of all subsets of A; A - Ø = A and A ∩ P(A) = {Ø, {Ø}, {b}, {Ø, b}}.
The full exam-length answer is in the app.
Let P and Q be the multisets where P = {5.a, 7.b, 8.c} and Q = {3.a, 5.b, 9.c}. Find: (i) P U Q (ii) Q - P.
P U Q = {5.a, 7.b, 8.c, 3.a, 5.b, 9.c} and Q - P = {3.a, 5.b, 9.c}.
The full exam-length answer is in the app.
Differentiate between proper subset and superset.
A proper subset is a subset that is not equal to the original set, while a superset contains all elements of the subset.
The full exam-length answer is in the app.
Define Greatest element and Least element in Hasse diagram.
The greatest element is the topmost element in a Hasse diagram, while the least element is the bottommost element.
The full exam-length answer is in the app.
Let A = {1, 2, 3, 4} and B = {a, b, c, d, e}. Compute the total number of possible relations from A to B.
The total number of possible relations from A to B is $2^{|A| imes |B|} = 2^{4 imes 5} = 2^{20} = 1048576$.
The full exam-length answer is in the app.
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.