(discrete mathematics for a computer programming course) Let p, q and r be the p

Question

(discrete mathematics for a computer programming course)

Let p, q and r be the propositions p: you get a recommendation on the end of the year, q: you work hard. r: you get promoted. Write the following propositions using p, q, and r and logical connectives. (a) You got promoted, but you do not work hard. (b) You get a recommendation on the end of the year, you work hard, and get promoted. (c) To get promoted, it is necessary for you to get a recommendation at the end of the year. (d) You get a recommendation on the end of the year, but you don't work hard; nevertheless, you get promoted. (e) Getting a recommendation on the end of the year and working hard is sufficient for getting promoted. (f) You will get promoted if and only if you work hard or you get a recommendation on the end of the year.

Explanation / Answer

Answer:

a) r ^ ~ q

b) p ^ q ^r

c) r ---> p

e) p---> r

f) (r <--->q) vp

Here the logical connectives used :

implication ( --->)

Bi implication

conjuction ( ^)

or ( V )

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