Question 9: From suitable properties of union and intersection, deduce the following results:
\((i)\) \(\;\) \(A\cap (A\cup B)=A\cup (A\cap B)\)
Solution:
\(\text{L.H.S.}=A\cap (A\cup B)\)
\(\ \ \ \ \ \ \ \ \ \ \ =[A\cap A]\cup[A\cap B)\) \(\quad\)\(\because\ \) distribution of intersection over union
\(\ \ \ \ \ \ \ \ \ \ \ =A\cup (A\cap B)\)
Hence, \(\text{L.H.S.}=\text{R.H.S.}\)