Question

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

Answer 1

Given : \(A ~\&~B\) are two sets

Let \(x~\in~A~\cap(A~\cup~B)\)

\(\Rightarrow~x~\in~A~\text{and}~x~\in~(A~\cup~B)\)

\(\Rightarrow~x~\in~A~\text{and}~(x~\in~A~or~x~\in~B)\)

\(\Rightarrow~(x~\in~A~\text{and}~x~\in~A)~or~(x~\in~A~\text{and}~x~\in~B)\)

\(\Rightarrow~x~\in~A~\text{or}~x~\in~(A~\text{and}~B)\)

\(\Rightarrow~x~\in~A\)

Hence, option (A) is correct.