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