# Given an example showing that, in general, (A U B) x (C U D) is not the same as (AXC)U(BXD). b) Consider the following (bogus) proof, which claims to show that (AUB) x (CUD) = (A x C) U (B x D). Identify the mistake. (m,y)€(A>

Given an example showing that, in general, (A U B) x (C U D) is not the same as

(AXC)U(BXD). b) Consider the following (bogus) proof, which claims to show that (AUB) x (CUD) =

(A x C) U (B x D). Identify the mistake. (m,y)€(A><C)U(B><D)

<—>(m,y)€AxCor(m,y)EB><D

<—>(mEAandyEC)or(mEBandyED)

H(m€AormEB)and(yECoryED)

H(mEAUB) and (yECUD) H(m,y) E (AUB) x (CUD). c) Give a correct proof of the fact that

(AXC)U(B xD)g (AUB) x (C’UD) for any sets A, B, C, D.

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The post Given an example showing that, in general, (A U B) x (C U D) is not the same as (AXC)U(BXD). b) Consider the following (bogus) proof, which claims to show that (AUB) x (CUD) = (A x C) U (B x D). Identify the mistake. (m,y)€(A><C)U(B><D) appeared first on Superb Professors.