17. Choose the property and evaluate the set operation

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

 

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

 

(ii) \(L\) \(\cup\) \((\)\(M\) \(\cup\) \(N\)\()\) \(=\) $\left\{i,i,i,i,i,i,i\right\}$.

 

[Note: Insert your answer in ascending order]