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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.