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

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1.Set Theory

easy

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

A

$A$

B

$B$

C

$\phi $

D

$A \cap {B^c}$

Solution

(d) $A \cap {(A \cap B)^c} = A \cap ({A^c} \cup {B^c})$

= $(A \cap {A^c}) \cup (A \cap {B^c})$ = $\phi \cup (A \cap {B^c}) = A \cap {B^c}$.

Standard 11

Mathematics

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