Discrete Mathematics with Graph Theory (3rd Edition) 17

Discrete Mathematics with Graph Theory (3rd Edition) 17 - F...

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Section 1.2 Exercises 1.2 1. 1. [BB] (Idempotence) The truth tables at the right show that p V P {:::::::} P and pAp {:::::::} p. Wlj PVP T T F F Wlj PI\P T T F F 2. (Commutativity) The truth tables show that p V q {:::::::} q V P and p A q {:::::::} q A p. p q pVq qVp P q pl\q ql\p T T T T T T T T T F T ·T T F F F F T T T F T F F F F F ." F F F F F 15 3. [BB] (Associativity) The equality of the fifth and seventh columns in the truth table shows that ((p V q) V r) {:::::::} (p V (q V r)). p q r pVq (pv q) Vr qVr pV(qVr) T T T T T T T T F T T .T T T F T T T -T T T F F T F T T T T T F T T T T T F F T T F T
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Unformatted text preview: F T F T T T T F F F F F F F The equality of the fifth and seventh . columns in the truth table shows that ((p A q) A r) {:::::::} (pA(qAr)). p q r pl\q (p f. ..q) 1\ r ql\r pl\(ql\r) T T T T T T T T F T F F F F F T T F F T F F F T F F F F T T F T F F F T F F F F F F F T F F F F F F F F F. F F F 4. (Distributivity) The equality of the fifth and eighth columns in the truth table shows thatp V (q A r) {:::::::} (PVq)A(pVr)). p q r ql\r pV(ql\r) pVq pVr (pVq) 1\ (pVr) T T T T T T T T T F ·T F T T T T F T T T T T T T F F T F F F T F .. T T F F T T T T T F F F T T T T F T F F F T F F F F F F .. F F F F...
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