Discrete Mathematics with Graph Theory (3rd Edition) 29

Discrete Mathematics with Graph Theory (3rd Edition) 29 -...

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Chapter 1 27 Together with ql, disjunctive syllogism gives (""Pl) V rl which is logically equivalent to Pl ---+ rl. Thus the given premises imply Pn ---+ rn which, again using 8(a), are logically equivalent to the single premise (pl ---+ rl) /\ (p2 ---+ r2) /\ ... /\ (pn ---+ rn). 10. [BB] In Latin, modus ponens means "method of affirming" and modus tollens means "method of denying". This is a reflection of the fact that modus tollens has a negative ...,p as its conclusion, while modus ponens affirms the truth of a statement q. Chapter 1 Review 1. P q r ...,r q ---+ (...,r) P /\ (q ---+ (...,r))
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Unformatted text preview: ...,q (...,q) V r T T T F F F F T T T F T T T F F T F T F T T T T F T T F F F F T T F F T T T T T F T F T T F F F F F T F T F 'T T F F F T T F T T (p /\ (q ---+ (...,r))) ---+ ((. ..,q) V r) T F T T T T T T 2. We have. ..,r is F, so (...,r) /\ s is F. Since q is T, this means q ---+ ((. ..,r) /\ s) is F. Butp is T, so P V (q ---+ ((. ..,r) /\ s)) is T. Also r /\ t is T. Hence the entire statement has truth value T. 3. (a) A truth table shows this is a contradiction. P q ...,q ...,p P /\ (...,q) (. ..,p)Vq [p /\ (...,q)]/\ [(. ..,p) V q] T T F F F T F T F T F T F F F T F T F T F F F T T F T F...
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