Discrete Mathematics with Graph Theory (3rd Edition) 21

Discrete Mathematics with Graph Theory (3rd Edition) 21 -...

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Unformatted text preview: Section 1.2 19 8. 1. [BB] The truth table shows that idempotence fails. p q p'::!..q q'::!..p UTIj P'::!..P T F F F T 2. Commutativity still holds. T F F T F T F p F T T F q r F T T F p Vq ( p V q) V r q Vr p V(q'::!..r) 3. [BB] Associativity holds. T T F. F T T F F T F T F T F T F T T T T F F F F F T T F F T T F T F F T F T T F F T F T T F T F T F F T F T T F 4. Just one distributive law holds. The table which follows shows that p 'i. (q 1\ r ) is not logically equivalent to (p 'i. q) 1\ (P'i. r), (p'::!.. q ) 1\ (p'::!.. r ) F On the other hand, (p 1\ (q 'i. r )) ~. (p 1\ q) 'i. (p 1\ r ) as shown. p q r q'::!..r p l\(q'::!..r) p l\q p l\r ( pl\q) '::!.. ( pl\r) T T F F T T F F T F T F T F T F T T T T F F F F F T F T T F. T F F T F F T F F F T F F F T F F F T T F F F F F F F T F F T F F F 6. Both laws o f D e Morgan fail. The tabl!! shows that -,(p 'i. q) is not logically equivalent to (-,p) 1\ (-,q). F The next table shows that -, (p 1\ q) is not logically equivalent to (-,p) 'i. (-,q). 7. [BB] The truth table shows that p 'i. 1 is no longer 1: ...
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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