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