Question

Read the statement shown below.

“If Annie is painting, then Joey is playing.”

Which of these is logically equivalent to the above statement? (6 points)
(0 pts) If Joey is not playing, then Annie is painting.
(6 pts) If Joey is not playing, then Annie is not painting.
(0 pts) If Annie is not painting, then Joey is playing.
(0 pts) If Annie is painting, then Joey is not playing.

Answer 1

I know the answer is B, but how do you solve this?

Answer 2

The contrapositive is logically equivalent to the conditional statement. In other words, if you SWITCH the statements and you NEGATE both statements, you will get a statement that is the same as your original statement.

Original: If Annie is painting, then Joey is playing.
Switch (Converse): If Joey is playing, then Annie is painting.
Switch + Negate (Contrapositive): If Joey is NOT playing, then Annie is NOT painting.

Answer 3

Thank you! That helped a bunch!

Answer 4

No problem :)