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Discrete Mathematics with Graph Theory (3rd Edition) 19

# Discrete Mathematics with Graph Theory (3rd Edition) 19 -...

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Section 1.2 11. [BB] The third and sixth columns of the truth table show that (p -t q) '¢=} ((-,q) -t (-,p)). 12. The third and sixth columns of the truth table show that (p ~ q) '¢=} ((p -t q) /\ (q -t p)). 13. [BB] The third and fifth columns 0 the truth table show that (p -t q) '¢=} ((-,p) V q). 2. (a) We construct a truth table. Since p V [-,(p /\ q)] is true for all values of p and q, this statement is a tautology. p q T T T F F T F F f p T T F F 17 p q p-+q -'q -'p (-,q) -+ (-,p) T T T F F T T F F T F F F T T F T T F F T T T T p ..... q p-+q q-+p (p -+ q) 1\ (q -+ p) T T T T F F T F F T F F T T T T p q p-+q -,p (-,p) V q T T T F T T F F F F F T T T T F F T T T q p/\q -,(p /\ q) P V [-,(p /\ q)] T T F T F F T T T F T T F F T T (b) By one of the laws of DeMorgan, the negation is (-,p) /\ (p /\ q). By associativity, this is logically equivalent to [( -,p) /\ p]/\ q '¢=} 0 /\ q '¢=} O. So the negation is a contradiction. 3. (a) [BB] Using one of the laws of De Morgan and one distributive property, we obtain
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