Question

Consider the following propositions: p: You get an A on the final exam. q: You do every exercise assigned in this course. r: You get an A in this class. (a) Translate the statement “You will get an A in this class if you do every exercise assigned in this course or you get an A on the final.” to propositional logic, using p, q, and r. (b) Write the truth table for the statement you wrote in (a). Is the statement a tautology? If not, provide a counter example. (c) What is the negation of the statement you wrote in (a)? (d) Write the truth table for the negation. For what combination(s) of values of p, q, and r is the negation true?

Answer 1

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Solution PYou get an A om the exam this couese do every exereise aosi an A m this class. You vey exexce an A on te final (a) You uill get an A this class assigned W this co wse ou do Treanslation: x-V P) Truth Table (VVP) (b) T F T Tt T T T F T F T T T T T ,this staliment not a No a staliment Yexat ia [Because a mo mattex ohatsove v tee caceT . Examal: pe) (yo) v (xop) TF TUL TT LL h

(C) +he stalemeut n (a) vo: natezap You will mot get an A m this class exeeise assigned m tis cowese and finale do not do uot an A m the Toranslahion: (dl) P F T F T F F T The ue ushen false all o them are false but a n trwe P,r ara true but ajand x felse P is tsuwe but a and r both arve bota asxce true but e io false p and V all thaee, Pray and e ase true FETETT 4 T D TT T - FTT