Discrete Mathematics with Graph Theory (3rd Edition) 14

Discrete Mathematics with Graph Theory (3rd Edition) 14 -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
12 Solutions to Exercises (e) p q r q->r p -> (q -> r) p/\q (p/\q)Vr (p -> (q -> r)) -> «p /\ q) V r) T T T T T T T T T F T T T F T T F T T T T F T T F F T T T F T T T T F F F T T T T F F T T F F F F T F F T F F F F F F T T F F F 2. (a) If p -> q is false, then necessarily p is true and q is false. (This is the only situation in which p -+ q is false.) We construct the relevant row of the truth table for (p 1\ (...,q)) V ((. ..,p) -+ q). I (p/\(.q)) ~ (.p)->q) I (b) [BB] There are three situations in which p -+ q is true. The question then is whether or not the truth value of (p 1\ ( ...,q)) V ((.p) -+ q) is the same in each of these cases. We construct a partial
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: truth table. p q .q p /\ (.q) .p (.p)->q (p/\ (.q)) V (.p) -> q) T T F F F T T F F T F T F F As shown, (p 1\ (.q)) V ((. ..,p) -+ q) has different truth values on two occasions where p -+ q is true, so it is not possible to answer the question in this case. 3. [BB] ~~~--+-~--~--~~~~~~~~-+~~~ F [p -+ (q /\ (.r))] V [r +-+ ((. ..,s) V q)] T 4. T [p -+ (q 1\ (...,r))] V [r +-+ ((. ..,s) V q)] T 5. (a) [BB] p q pl\q pVq (p 1\ q) -+ (p V q) T T T T T T F F T T F T F T T F F F F T The final column shows that (p /\ q) -+ (p V q) is true for all values of p and q, so this statement is a tautology....
View Full Document

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.

Ask a homework question - tutors are online