If A and B are two given sets, then A (A )^c is equal to: - Vidyadip

MCQ

If $A$ and $B$ are two given sets, then $\text{A}\cap\text{(A}\cap\text{B})^\text{c}$ is equal to:

A
$\text{A}$
B
$\text{B}$
C
$\phi$
✓
$\text{A}\cap\text{B}^\text{c}.$

✓

Answer

Correct option: D.

$\text{A}\cap\text{B}^\text{c}.$

$A$ and $B$ are two sets.
$\text{A}\cap\text{B}$ is the common region in both the sets.
$\text{A}\cap\text{B}^\text{c}$ is all the region in the universal set except $\text{A}\cap\text{B}.$
Now,
$\text{(A}\cap\text{A}\cap\text{B)}^\text{c}=\text{(A}\cap\text{B)}^\text{c}.$

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