Question

Write a conditional statement for this Venn diagram.



(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.**