Write a conditional statement for this Venn diagram.

Question

(1 point)
Responses which answer is correct and why

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.
Video Player

Question 2
Write a counterexample for the converse.(1 point)
Responses which answer is correct and why

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 address your request regarding the Venn diagram and the conditional statement, let's first clarify what the original statement implies.

Conditional Statement for the Venn Diagram

From your description, it seems that the relationship you are describing is:

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

In formal logical terms, this can be stated as:

• If it is red, then it is a color. (This corresponds to the statement “If P, then Q”, where P is "it is red" and Q is "it is a color.")

Counterexample for the Converse

The converse of the original statement would be:

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

To find a counterexample, we need an instance where an object is a color but not red.

Here are your options evaluated:

1. Blue is a color. - This is a correct counterexample, as blue is a color, and it is not red.
2. Red is also a flavor of Gatorade. - This does not serve as a counterexample because it does not pertain to colors, just an attribute of red.
3. Red is not a color. - This contradicts the accepted definition of colors; hence, it is not a valid option.
4. There is no counterexample, because the converse is also true. - This is incorrect, as the converse is not universally true (as shown by the counterexample).

Conclusion

• The correct conditional statement is: If it is red, then it is a color.
• The best counterexample for the converse is: Blue is a color.