9. Find using commutative property

If \(X\) \(=\) \(\{\)\(y\) : \(y\) \(=\) $5^n$, \(n \in \mathbb{N}\) and \(n \le 3\}\), \(Y\) \(=\) \(\{\)\(y\) : \(y\) \(=\) $5n$, \(n \in \mathbb{N}\) and \(n \le 3\}\), then find the following.

 

(i) Commutative property of intersection of sets: \(X\) \(\cup\) \(Y\) \(=\) \(Y\) \(\cup\) \(X\)\(X\) \(\cup\) (\(Y\) \(\cap\) \(=\) (\(X\) \(\cup\) \(Y\)) \(\cap\) \(X\) \(\cap\) \(Y\) \(=\) \(Y\) \(\cap\) \(X\)\(X\) \(\cap\) (\(Y\) \(\cup\) ) \(=\) (\(X\) \(\cap\) \(Y\)) \(\cup\)

 

(ii) \(Y\) \(\cap\) \(X\) \(=\) \(\{\)\(5\), \(10\), \(15\), \(25\)\(\}\)\(\{\)\(5\), \(25\), \(125\)\(\}\)\(\{5\}\)\(\{\)\(5\), \(10\), \(15\), \(25\), \(125\)\(\}\)