Question

Let p and q be 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.

1. You do not drive over 65 miles per hour.
2. You will get a speeding ticket if you drive over 65 miles per hour.
3. If you do not drive over 65 miles per hour, then you will not get a speeding ticket. 

Answer 1

p: You drive over 65 miles per hour. 

q: You get a speeding ticket.

1) You do not drive over 65 miles per hour:

$\neg p$

2) You will get a speeding ticket if you drive over 65 miles per hour:

$p\to q$

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

$\neg p \to \neg q$