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Write a conditional statement for this Venn diagram.

Choose the correct answers carefully

(1 point)
Responses

Red is a color
Red is a color

It is red, if and only if it is a color.
It is red, if and only if it is a color.

If it is red, then is is a color.
If it is red, then is is a color.

All colors are red.
All colors are red.
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Question 2
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.
There is no counterexample, because the converse is also true.
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1 answer

To help you choose the correct responses based on the conditional statements and the converse, I'll break down the options you've provided.

Question 1

The options for the conditional statement regarding the Venn diagram seem to focus on the relationship between red and color:

  1. Red is a color.
  2. It is red, if and only if it is a color.
  3. If it is red, then it is a color.
  4. All colors are red.

The best choice for a conditional statement is: - If it is red, then it is a color.

This implies that being red is a sufficient condition for being a color, which aligns with common understanding.

Question 2

For a counterexample of the converse, we first establish the original conditional statement, which can be stated as:

  • If something is red, then it is a color.

The converse of this statement is:

  • If something is a color, then it is red.

To find a counterexample for the converse, we need to identify a color that is not red.

The best option for a counterexample from your responses is: - Blue is a color.

This is because, while blue is a color, it is not red, thereby demonstrating that the converse is not true.

Summary:

  • Question 1: If it is red, then it is a color.
  • Question 2: Blue is a color.