Kenneth Rosen Edition 6th Exercise 1.1 Question 9 (Page No. 17)

Question

Let p and q be the propositions
p : You drive over 65 miles per hour.
q : You get a speeding ticket.
Write these propositions using p and q and logical connectives (including negations).

• A. You do not drive over 65 miles per hour.
• B. You drive over 65 miles per hour, but you do not get a speeding ticket.
• C. You will get a speeding ticket if you drive over 65 miles per hour.
• D. If you do not drive over 65 miles per hour, then you will not get a speeding ticket.
• E. Driving over 65 miles per hour is sufficient for getting a speeding ticket.
• F. You get a speeding ticket, but you do not drive over 65 miles per hour.
• G. Whenever you get a speeding ticket, you are driving over 65 miles per hour.

Answer 1

A) ~P

B) P⋀ ~Q

C) P-->Q

D)~P-->~Q

E)P-->Q

F)~P⋀Q

G)Q-->P