# 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&gt;&lt;C)U(B&gt;&lt;D)
&lt;—&gt;(m,y)€AxCor(m,y)EB&gt;&lt;D
&lt;—&gt;(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.