Let A, B, C, D be sets. (a) Suppose that A, B, C, D are all non-empty. Is it true that A x B = C x D implies A = C and B = D? Either prove the claim or provide a counterexample. (b) Now drop the assumption that A, B, C, D are all non-empty, and repeat part (a).

Let A, B, C, D be sets. (a) Suppose that A, B, C, D are all non-empty. Is it true that A x B = C x D implies A = C and B = D? Either prove the claim or provide a counterexample. (b) Now drop the assumption that A, B, C, D are all non-empty, and repeat part (a).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 4CR

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Question

Let A, B, C, D be sets.
(a) Suppose that A, B, C, D are all non-empty. Is it true that A x B = C x D implies A = C and
B = D? Either prove the claim or provide a counterexample.
(b) Now drop the assumption that A, B, C, D are all non-empty, and repeat part (a).

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Step 2: Prove the claim , when A,B,C,D are all non empty.

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Step 3: Consider B and C are empty

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