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Question

Which answers are correct and why

Question 1
Write a conditional statement for this Venn diagram.

(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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Answer 1

Let's analyze each question and discuss which answers are correct and why.

Question 1:

Write a conditional statement for this Venn diagram.

Responses:

1. Red is a color - This is a statement, but not a conditional form.
2. It is red, if and only if it is a color. - This is a biconditional statement. It implies that being red and being a color are equivalent, which is stronger than what a Venn diagram might typically show.
3. If it is red, then it is a color. - This is a proper conditional statement. It states that if something is red, then it falls into the category of colors, aligning well with typical interpretations of Venn diagrams where red is a subset of colors.
4. All colors are red. - This is not true in general and does not reflect the conditions typically depicted in a Venn diagram. It incorrectly implies that colors are exclusively red.

Correct Answer: If it is red, then it is a color.

Question 2:

Write a counterexample for the converse.

Responses:

1. Blue is a color. - This does not serve as a counterexample; it simply states something that is true.
2. Red is also a flavor of Gatorade. - This is irrelevant to the discussion about a counterexample for a converse.
3. Red is not a color. - This could potentially serve as a counterexample, but it is factually incorrect because red is indeed a color. However, if the converse of the original statement is something like "If it is a color, then it is red," then this option would work as a counterexample (since there are many colors that are not red).
4. There is no counterexample because the converse is also true. - Depending on what the original statement is, this might not be accurate. For example, if the original statement is "If it is red, then it is a color," the converse "If it is a color, then it is red" is not necessarily true, indicating that a counterexample does exist.

Correct Answer: Red is not a color. (Assuming the converse was "If it is a color, then it is red.") This technically would illustrate the fallacy of the converse with specific color examples.

Summary:

• For Question 1, select “If it is red, then it is a color.”
• For Question 2, while the effective answer could vary depending on context, a suggestion would be “Red is not a color,” assuming the original conditional statement was about red being a color vs. other colors.