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Discrete Mathematics with Graph Theory (3rd Edition) 27

# Discrete Mathematics with Graph Theory (3rd Edition) 27 - T...

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Section 1.3 The given argument is p-+q q -+ r . r-+p This is not valid, as the truth table shows. In row five, the two premises are true but the conclusion is false. p q T T T F F T F F T T T F F T F F p: I work hard r p~q T T T F T T T T F T F F F T F T (h) Let p, q, and r be the statements q: I earn lots of money r : I pay high taxes. p-+q The given argument is q -+ r . p-+r This is valid by the chain rule. p: I work hard (i) Let p, q, and r be the statements q: I earn lots of money r : I pay high taxes. p-+q The given argument is q-+r ""p -+...,r q~r T T T T F T F T r~p T T F F T
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Unformatted text preview: T T * * * * 25 The conclusion is logically equivalent to r -+ p, so this is the same as Exercise 5(g), hence not valid. p: (j) Let p, q, and r be the statements q: r: The given argument is p-+q ...,q pVr . r I like mathematics I study I like football. The first two premises give ...,p by modus tollens, so, since p V r is true, the conclusion follows by disjunctive syllogism. p: (k) Let p, q, and r be the statements q: r: qVr The given argument is r -+ p (...,q) -+ p qVr I like mathematics I study I like football. This is the same as ( ...,r) V p and hence valid by resolution. qVp...
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