New Exam Prep
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New Exam Prep
Sample questions with model answers
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Let $A = \{1, 2, 3, 4\}$. Find the power set of $A$. Give an example of a relation that is reflexive and symmetric but not transitive.
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Power set of A is \{\emptyset, \{1\}, \{2\}, \{3\}, \{4\}, \{1,2\}, \{1,3\}, \{1,4\}, \{2,3\}, \{2,4\}, \{3,4\}, \{1,2,3\}, \{1,2,4\}, \{1,3,4\}, \{2,3,4\}, \{1,2,3,4\}\}. Example relation: R = \{(1,1), (2,2), (1,2), (2,1)\}.
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For each of the following functions, determine if it is injective (one-to-one), surjective (onto), and/or bijective. Justify your answer. 1. $f: Z \to Z$ defined by $f(x) = x^2$ 2. $g: R \to R$ defined by $g(x) = 2x - 3$
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1. f is not injective, surjective, or bijective. 2. g is injective and surjective, hence bijective.
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Simplify the following Boolean expression using a 4-variable Karnaugh map: $F(A, B, C, D) = \sum m(0, 2, 5, 6, 7, 8, 10, 13, 15)$ Where $\sum m$ indicates the sum of minterms.
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Simplified expression is obtained from the Karnaugh map.
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In how many ways can a team of 5 students be chosen from a group of 8 boys and 6 girls if the team must contain at least 2 girls?
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Total ways = C(6,2)*C(8,3) + C(6,3)*C(8,2) + C(6,4)*C(8,1) + C(6,5)*C(8,0).
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