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Question

If U={4,8,12,16,20,24,28},A={8,16,24},B={4,16,20,28}.
Verify that (AB)=AB

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Solution

The given sets are U={4,8,12,16,20,24,28}, A={8,16,24} and B={4,16,20,28}

We know that the complement of set A is A=UA.

Consider the following:

(AB)=U(AB)={4,8,12,16,20,24,28}[{8,16,24}{4,16,20,28}]
={4,8,12,16,20,24,28}{4,8,16,20,24,28}={12}......(1)

AB=[UA][UB]=[{4,8,12,16,20,24,28}{8,16,24}][{4,8,12,16,20,24,28}{4,16,20,28}]
={4,12,20,28}{8,12,24}={12}......(2)

From equations 1 and 2, we get that (AB)=AB.

Hence, (AB)=AB.


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