Discrete Mathematics with Graph Theory (3rd Edition) 15

Discrete Mathematics with Graph Theory (3rd Edition) 15 - T...

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Section 1.1 13 (b) [BB] p q -,p (-,p) A q -,q pV (-,q) ((-,p) A q) A (p V (-,q)) T T F F F T F T F F F T T F F T T T F F F F F T F T T F The final column shows that (( -,p) A q) A (p V (-,q)) is false for all values of p and q, so this statement is a contradiction. 6. (a) (b) p q p-+q T T T T F F F T T F F T p q pl\.q T T T T F F F T F F F F q -+ (p -+ q) T T T T -'p -.q « -.p) V (-.q)) F F F F T T T F T T T T Since q - (p - q all values of p and ) is true for q,this logy. statement is a tauto (pl\.q) I\. [(-,p) V (-.q)] F F F F Since (p A q) A (( -,p) V (-,q)) is false for all values of p and q, this statement is a contradiction. 7. (a) [BB] (p -+ q) I\. (q -+ r) p q r p-+q q-+r T T T T T T F T F T F T T T T F F T T
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Unformatted text preview: T T T F T F T F F F T F T F T F F F F T T [(p -+ q) I\. (q -+ r)] -+ [p -+ r] T T T T T T T T p-+r T T F. T T T T T F F F F F T T T Since [(p -q) A (q -r)] -[p - r] is true for all ement is a tautology. values of p, q, and r, this stat (b) [BB] If p implies q which, in turn, implies r, then certainly p implies r. 8. We must show that the given "or" statement can be both true and false. We construct truth tables for each part of the "or" and show that certain identical values for the variables make both parts T (so that the "or" is true) and other certain identical values for the variables make both parts F (so that the "or" is false). p r 8 -.r -'8 (-.r) -+ (-'8) pV [(-.r) -+ (-'8)] T T T F F T T F F T T F F F...
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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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