MATH 221 Study Guide - Midterm Guide: Joule, Bijection, Surjective Function
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Solution. (a) jan is either not rich or not happy. (b) carlos will neither bicycle nor run tomorrow. (c) mei neither walks nor takes the bus to class. (d) ibrahim is either not smart or not hard working. Solution. (a) we have p q p q p q p q p q (p q) ( p q) Since p q and (p q) ( p q) take the same truth values for all p. 0 and q, they are logically equivalent. domain consists of all real numbers. (b) if p = 1, q = 0, r = 0, then (p q) r = 1 and (p r) (q r) = 0. Therefore, (p q) r and (p r) (q r) are not logically equivalent. Determine the truth value of each of these statements if the (a) x(x3 = 1). (b) x(x4 < x2). (c) x(( x)2 = x2). (d) x(2x > x).
