For any two sets A and B, A (A )= 1. A 2. B 3. 4. None of these. - Vidyadip

Question

For any two sets A and B, $\text{A}\cap\text{(A}\cup\text{B)}=$

A
B
$\phi$
None of these.

✓

Answer

A.

Solution:

$\text{A}\cap\text{(A}\cup\text{B)}=\text{(A}\cap\text{A)}\cup\text{(A}\cap\text{B)}=\text{A}\cup\text{(A}\cap\text{B)}=\\\text{AA}\cap\text{(A}\cup\text{B)}=\text{(A}\cap\text{A)}\cup\text{(A}\cap\text{B)}=\text{A}\cup\text{(A}\cap\text{B)}=\text{A.}$

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