3. (12') Using Venn diagrams, verify the following identities. (a) A-(AnB)U(A-B) ( b) If A and...

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Question

3. (12) Using Venn diagrams, verify the following identities. (a) A-(AnB)U(A-B) ( b) If A and B are finite sets, we have (AUB)- A+B-(AnB )

Answer 1

Answer #1

(a) From the Venn Diagram, we can see that the shaded region of (A cap B) U (A - B) = A

An B A-B

(b) As given in the Venn Diagram below, the overlapping portion of A U B = A cap B.

AnB (Overlapping)

So, A cap B is overlapped in A and B and hence, it is subtracted so that that region is not counted twice.

Answer 2

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