Computer Science 2214A/B Study Guide - Final Guide: Propositional Calculus, Logical Equivalence, Contraposition
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2 Mar 2021
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Problem 1 suppose the variable s represents students, c represents courses, and t (s, c) means s is taking c . Solution 1: ( c)( s) t (s, c), ( s)( c) t (s, c), ( s)( c) t (s, c), ( c)( s) t (s, c), ( s)( c) t (s, c), ( c)( s) t (s, c), ( s)( c) t (s, c), ( c)( s) t (s, c), 1: ( c)( s) t (s, c), ( s)( c) t (s, c). Problem 2 prove that the following is true for all positive integers n: n is even if and only if 3n2 + 8 is even . Solution 2: we rst prove that if n is even then so is 3n2+8. Hence we assume that n is even and deduce that 3n2 + 8 is even as well. The assumption means that there exists an integer k such that n = 2 k holds.