- (i) Use a counter example to show that the following statement is false
$$\text { " } n ^ { 2 } + 3 n + 1 \text { is prime for all } n \in \mathbb { N } \text { " }$$
(ii) Use algebra to prove by exhaustion that for all \(n \in \mathbb { N }\)
$$\text { " } n ^ { 2 } - 2 \text { is not a multiple of } 4 \text { " }$$