Write a counterexample for the converse.(1 point)

Responses

Blue is a color.
Blue is a color.

Red is also a flavor of Gatorade.
Red is also a flavor of Gatorade.

Red is not a color.
Red is not a color.

There is no counterexample, because the converse is also true.

1 answer

To provide a counterexample for the converse, we first need to clarify the original statement and its converse.

Original statement (P → Q): "If something is blue (P), then it is a color (Q)."

Converse statement (Q → P): "If something is a color (Q), then it is blue (P)."

The original statement is true, as blue is indeed a color. However, the converse statement is not necessarily true, as there are many other colors besides blue.

A counterexample for the converse would be:

"A red apple is a color, but it is not blue."

This demonstrates that the converse (Q → P) is false because not all colors are blue. Therefore, the correct response would be:

Red is also a color, but it is not blue.