10. Solve using commutative property

If \(L\) \(=\) \(\{\)\(z\) : \(z\) \(=\) $6^n$, \(n \in \mathbb{N}\) and \(n \le 3\}\), \(M\) \(=\) \(\{\)\(z\) : \(z\) \(=\) $6n$, \(n \in \mathbb{N}\) and \(n \le 3\}\), then find the following:

 

(i) Commutative property of union of sets: \(L\)\(\cap\)(\(M\)\(\cup\)\(N\)) \(=\) (\(L\)\(\cap\)\(M\))\(\cup\)\(N\)\(L\)\(\cup\)(\(M\)\(\cap\)\(N\)) \(=\) (\(L\)\(\cup\)\(M\))\(\cap\)\(N\)\(L\)\(\cap\)\(M\) \(=\) \(M\)\(\cap\)\(L\)\(L\)\(\cup\)\(M\) \(=\) \(M\)\(\cup\)\(L\)

 

(ii) \(M\) \(\cup\) \(L\) \(=\) \(\{\)\(6\)\(\}\)\(\{\)\(6\), \(12\), \(18\), \(36\), \(216\)\(\}\)\(\{\)\(6\), \(12\), \(18\), \(36\)\(\}\)\(\{\)\(6\), \(12\), \(18\)\(\}\)