EXAMPLE 2.2.7

Select that statement that is logically equivalent to: "If you don't carry an umbrella, you'll get soaked."

A. You carry an umbrella and you won't get soaked.

B. You carry an umbrella or you get soaked.

C. You don't carry an umbrella and you get soaked.

D. You don't carry an umbrella or you get soaked.

E. You leave your umbrella in the classroom, so you get soaked anyway.

SOLUTION

Let p be the statement "You don't carry an umbrella."

Let q be the statement "You'll get soaked."

The statement "If you don't carry an umbrella, you'll get soaked" has the form "If p, then q." This is logically equivalent to "Not p, or q." The correct choice is "B. You carry an umbrella or you get soaked."