Answer to Question #168694 in Discrete Mathematics for zhihui

Question

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)

Answer 1

(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: $(p \land q) \land \neg r$