Theorem? Proof. Please explain how it is correct or how it can be fixed. For any
ID: 3079466 • Letter: T
Question
Theorem?
Proof.
Please explain how it is correct or how it can be fixed.
For any sets A, B, C, and D, if A times B C times D then A C and B D. Is the following proof correct? If so, what proof strategies does it use? If not, can it be fixed? Is the theorem correct? Suppose A times B C times D. Let a be an arbitrary element of A and let b be an arbitrary element of B. Then (a, b) epsilon A times B. Since A times B C times D, (a, b) epsilon C times D. Therefore a epsilon C and b epsilon D. Since a and b were arbitrary elements of A and B, respectively, this shows that A C and B D.Explanation / Answer
The theorem and proof are both valid.
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