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Unformatted text preview: A ----+ '13 false and '13 ----+ A true, contradicting logical equivalence. So '13 must be true also. Similarly, if '13 is true, then A must also be true. We conclude that A is true if and only if '13 is true. This means A and '13 are logically equivalent. 5. (a) Since A <==> '13, we know that A is true precisely when '13 is true. Since '13 <==> e, '13 is true precisely when e is true. Hence A is true if and only if e is true, that is, A <==> e. (b) Property 12 says (p ----+ q) <==> «-.p) V q). Clearly, «-.p) V q) <==> (q V (-.p)) , so part (a) tells us (p ----+ q) <==> (q V (-.p)). But Property 12 also says «-.q) ----+ (-.p)) <==> (-.(-.q) V (-.p)) and clearly (-. ( -.q) V (-.p)) <==> (q V (-.p)). So we have (p ----+ q) <==> (q V (-.p)) and also...
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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.
- Summer '10
- Graph Theory