If A and B are two sets, then A (A B) equals - Vidyadip

MCQ

If $A$ and $B$ are two sets, then $A \cap(A \cup B)$ equals

A
$B$
B
$\phi$
✓
$A$
D
$A \cap B$

✓

Answer

Correct option: C.

$A$

Let us assume that $x \in A \cap(A \cup B)$
$\Rightarrow x \in A$ and $x \in(A \cup B)$
$\Rightarrow x \in A$ and $(x \in A$ or $x \in B)$
$\Rightarrow(x \in A$ and $x \in A)$ or $(x \in A$ and $x \in B)$
$\Rightarrow x \in A $ or $x \in A \cap B$
$\Rightarrow x \in A$
Therefore, $A \cap(A \cup B)=A$

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