7. Choose the property and evaluate the set operation

If \(P\) \(=\) \(\{\)\(y\) : \(y\) \(=\) $2^n$, \(n \in \mathbb{W}\) and \(n \le 3\}\), \(Q\) \(=\) \(\{\)\(y\) : \(y\) \(=\) $2n$, \(n \in \mathbb{N}\) and \(n \le 4\}\) and \(R\) \(=\) \(\{\)\(0\), \(1\), \(2\), \(4\), \(7\)\(\}\), then evaluate the following:

 

(i) Associative property of union of sets: \(P\) \(\cup\) \(Q\) \(=\) \(Q\) \(\cup\) \(R\)\(P\) \(\cap\) \(Q\) \(=\) \(Q\) \(\cap\) \(P\)\(P\) \(\cap\) \((\)\(Q\) \(\cup\) \(R\)\()\) \(=\) \((\)\(P\) \(\cap\) \(Q\)\()\) \(\cup\) \(R\)\(P\) \(\cup\) \((\)\(Q\) \(\cup\) \(R\)\()\) \(=\) \((\)\(P\) \(\cup\) \(Q\)\()\) \(\cup\) \(R\)

 

(ii) \((\)\(P\) \(\cup\) \(Q\)\()\) \(\cup\) \(R\) \(=\) $\left\{i,i,i,i,i,i,i\right\}$.

 

[Note: Insert your answer in ascending order]