Question

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

Logical expressions are expressions that connect two or more different sentences (prepositions) together in a way that they make grammatical sense. This is done by logical connectors.

To answer the highlighted questions directly

Let

P: You drive over 65 miles per hour

q: You get a speeding ticket

~P: You do not drive over 65 miles per hour

~q: You do not get a speeding ticket

(a) p ∧ ~q

(b) ~p→~q

(c) q ∧ ~p