4. (2.5 8 = 20 points) Let p, q, and r be the propositions

p: You get a signing bonus.

q: You receive a higher salary.

r: You take the job offer.

Write these propositions using p, q, and r and logical connectives including negation. (For some of the problems refer to the list of common ways to express conditional statements provided in Section 1.1.)

a) You take the job offer, but you do not receive a higher salary.

b) To take the job offer, it is necessary for you to get a signing bonus.

c) You do not receive a higher salary, but you get a signing bonus and take the job offer.

d) You receive a higher salary whenever you get a signing bonus.

e) You get a signing bonus only if you take the job offer.

f) You take the job offer if and only if you either get a signing bonus or receive a higher salary.

g) A sufficient condition for you to take the job offer is to receive a higher salary.

h) You receive a higher salary unless you get a signing bonus.

9. (4 points) Translate the following statement into propositional logic using the propositions provided:

It is necessary to scan the email for viruses whenever it was from an unknown sender or it contains an attachment.

Express your answer in terms of a: The email contains an attachment, s: The email is scanned for viruses, and u: The email was from an unknown sender.