Write a conditional statement for this Venn diagram

Question

The Venn diagram is a small circle labeled "red" inside a bigger circle labeled "color"

Red is a color
It is red, if and only if it is a color
If it is red, then it is a color
All colors are red

Write a counterexample for the converse

Blue is a color
Red is also a flavor of gatorade
Red is not a color
There is no counterexample, because the converse is also true

Answer 1

Based on the description of the Venn diagram and the provided statements, we can summarize the relationships as follows:

Conditional Statement: If something is red, then it is a color.

This can be written formally as:

• If \( x \) is red, then \( x \) is a color.

Converse Statement: If something is a color, then it is red.

This can be written formally as:

• If \( x \) is a color, then \( x \) is red.

Counterexample for the Converse: To provide a counterexample for the converse, we need to find an object or instance that is a color but is not red.

Counterexample:

• The color blue is a color, but it is not red.

Since blue satisfies the condition of being a color, but it does not fall into the category of red, it serves as a counterexample to prove that the converse statement (If something is a color, then it is red) is not universally true.

Thus, the statement "All colors are red" is false, demonstrating that the converse does not hold in all cases.