Write a counterexample for the converse.(1 point)

Question

Responses which answer is correct and why by explaining

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.

Answer 1

To clarify your request, let's first define what a converse is. In a statement of the form "If \( P \), then \( Q \)" (denoted as \( P \to Q \)), the converse is "If \( Q \), then \( P \)" (denoted as \( Q \to P \)).

Let's consider a statement and its converse:

1. Original statement: If something is red, then it is a color. (If \( P \), then \( Q \))
2. Converse statement: If something is a color, then it is red. (If \( Q \), then \( P \))

Counterexample for the converse:

• A counterexample would be any color that is not red. For instance, blue is a color but it is not red.

So, the explanation for why this counterexample works is: The original statement "If something is red, then it is a color" is true because red is indeed a color. However, the converse "If something is a color, then it is red" is not universally true because there are many other colors (like blue, green, yellow, etc.) that qualify as colors but are not red. Therefore, the converse statement does not hold, and our counterexample (blue) effectively disproves it.