MATH-0061 Final: Math 61-02 Final Exam Solution
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P q r ((p q) r) F (p (q r)) (p (q r)) ((p q) (p r)) Alternately, here is an argument without truth tables: (a) if ((p q) r), we have that either (a) exactly one of p or q is true, or (b) r is true, but not both (a) and (b). 3 for all n n (c) if a1, a2, . , an, b are sets (n 1), then si [n] Show that n n, f 2 (ai \ b) = ( si [n] Ai) \ b. n = fnfn+1. (d) let fn denote the nth term of the fibonacci sequence (where f1 = 1, f2 = 1, and fk = 1 2 + 2 3 + + k (k + 1) + (k + 1) (k + 2) = k(k + 1)(k + 2) + (k + 1) (k + 2) k(k + 1)(k + 2)
