Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 41 Mark
MCQ
If $A$ and $B$ are two sets, then $A \cap(A \cup B)$ equals
A
B
B
$\phi$
C
A
D
$A \cap B$
✓
Answer
(c) A Explanation: Let us assume that $x \in A \cap(A \cup B)$ $\begin{array}{l}\Rightarrow x \in A \text { and } x \in(A \cup B) \\ \Rightarrow x \in A \text { and }(x \in A \text { or } x \in B) \\ \Rightarrow(x \in A \text { and } x \in A) \text { or }(x \in A \text { and } x \in B) \\ \Rightarrow x \in A \text { or } x \in A \cap B \\ \Rightarrow x \in A\end{array}$ Therefore, $A \cap(A \cup B)=A$
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