Q.(i) Write the negation of the statement "Every natural number is greater than zero".

Negation reverses a universal (every) statement into an existential (there exists ... not) statement. Converse swaps hypothesis and conclusion; contrapositive negates and swaps both.

1. Negation Original: every natural number is greater than zero. This has the form: for all $n$, $P(n)$, where $P(n)$ means $n$ is greater than zero. The negation of for all $n$, $P(n)$ is there exists $n$ such that not $P(n)$: $\text{Negation: There exists a natural number that is not greater than zero.}$
2. Converse and contrapositive Original statement: if $n^2$ is even then $n$ is even. This has the form if $p$ then $q$, with $p$ meaning $n^2$ is even, $q$ meaning $n$ is even. Converse (if $q$ then $p$): $\text{If } n \text{ is even, then } n^2 \text{ is even.}$ …