For any two sets A and B, A (A )' is equal to: - Vidyadip

MCQ

For any two sets A and B, $\text{A}\cap\text{(A}\cup\text{B)}'$ is equal to:

A
$\text{A}$
B
$\text{B}$
C
$\phi$
D
$\text{A}\cap\text{B}.$

✓

Answer

$\phi.$

Solution:

$\text{A}\cap\text{(A}\cup\text{B)}'$

$=\text{A}\cap\text{(A}'\cup\text{B}')$ (De Morgen Law)

$=\text{(A}\cap\text{A}')\cap\text{B}'$

$=\phi\cap\text{B}'$

$=\phi$

Hence, the correct answer is option (c).

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