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Question

Using properties of sets, show that
(i) A(AB)=A (ii) A(AB)=A

Solution
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(i) To show: A(AB)=A
We know that
AA
ABA
A(AB)A ......(1)
Also, AA(AB) ............(2)
From (1) and (2),
A(AB)=A
(ii) To show: A(AB)=A
A(AB)=(AA)(AB)
=A(AB)
=A (by (i))
A(AB)=A

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