Question
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.
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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To provide a counterexample for the converse, we first need to clarify the original statement and its converse.
Original statement (P → Q): "If something is blue (P), then it is a color (Q)."
Converse statement (Q → P): "If something is a color (Q), then it is blue (P)."
The original statement is true, as blue is indeed a color. However, the converse statement is not necessarily true, as there are many other colors besides blue.
A counterexample for the converse would be:
"A red apple is a color, but it is not blue."
This demonstrates that the converse (Q → P) is false because not all colors are blue. Therefore, the correct response would be:
**Red is also a color, but it is not blue.**
Original statement (P → Q): "If something is blue (P), then it is a color (Q)."
Converse statement (Q → P): "If something is a color (Q), then it is blue (P)."
The original statement is true, as blue is indeed a color. However, the converse statement is not necessarily true, as there are many other colors besides blue.
A counterexample for the converse would be:
"A red apple is a color, but it is not blue."
This demonstrates that the converse (Q → P) is false because not all colors are blue. Therefore, the correct response would be:
**Red is also a color, but it is not blue.**
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