If A and B are two sets, then A cap (A cup B)' is equal to

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1.Set Theory

medium

If $A$ and $B$ are two sets, then $A \cap (A \cup B)'$ is equal to

A

$A$

B

$B$

C

$\phi $

D

None of these

Solution

(c) $A \cap (A \cup B)' = A \cap (A' \cap B')$,$(\because (A \cup B)' = A' \cap B'\,)$

$ = (A \cap A') \cap B'$, (by associative law)

$ = \phi \cap B'$,$(\because A \cap A' = \phi )$

$ = \phi $.

Standard 11

Mathematics

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