Question

Define the following propositions: .p: You drive over 65 miles per hour q You get a speeding ticket Translate the following English sentence into logical expressions using the definitions above (a) You drive over 65 miles per hour, but you do not get a speeding ticket. (b) If you do not drive over 65 miles per hour, then you will not get a speeding ticket (c) You get a speeding ticket, but you did not drive over 65 miles per hour.

Answer 1

Answer:

a.p→¬q

b.¬p→¬q

c.q→¬p

Step-by-step explanation:

p:You drive over 65 miles per hour

¬p: You do not drive over 65 miles per hour

q:You get a speeding ticket

¬q:You do not get a speeding ticket

(a) You drive over 65 miles per hour, but you do not get a speeding ticket

the first sentence is p and because the consequence is the opposite of q then is no q

p→¬q

(b) If you do not drive over 65 miles per hour, then you will not get a speeding ticket

The first sentence is the opposite of p (¬p), and the second sentence is the opposite of q

¬p→¬q

(c) You get a speeding ticket, but you did not drive over 65 miles per hour.

The first one is q, and the second one is the opposite of p so

q→¬p