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  • If A and B are two sets, then A ∩ (A ∪ B) equals (A) A (B) B (C) φ (D) A ∩ B

If A and B are two sets, then A ∩ (A ∪ B) equals

(A) A (B) B (C) \phi (D) (A ∪ B)

Answers (1)

The answer is the option (a).  Let x\in A\cap (A\cup B)

\begin{aligned} \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\end{aligned}

Hence A is correct.

Posted by

infoexpert22

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