Solution to Question 1 Let p: I get the job q: I work hard r: I get … - Sikademy
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Archangel Macsika

Question 1 Let p: I get the job q: I work hard r: I get promoted (a) Write the following proposition in terms of p, q, r and logical connectives. “If I get the job and work hard, then I will get promoted.” (2 marks) (b) Use your answer in part (i), state the converse, contrapositive and negation of the proposition in terms of p, q, r and logical connectives. Simplify your answers to the form without logical connectives “→”. (6 marks)

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(a) (p \land q) \to r

Simplify: (\neg p \lor \neg q) \lor r

(b) Converse: r \to (p \land q)

Simplify: \neg r \lor (p \land q)

Contrapositive: \neg (p \land q) \to \neg r

Simplify: (p \land q) \lor \neg r

Negation: \neg ((p \land q) \to r)

Simplify: (p \land q) \land \neg r

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Question ID: mtid-5-stid-8-sqid-3331-qpid-2030