I made an attempt on this question. Please guide me if its wrong.
Consider the following boolean fuctions: $\sim p$ ,$\sim\sim\sim\sim\sim p$ , and $\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim p$ . Which of these are equal?
$\sim p$ and $\sim\sim\sim\sim\sim p$ are equal since if we write $\sim\sim p$, then this can be simplified to give $p$ as double negation canceled out or we can say $\sim\sim p=p$. Thus, in $\sim\sim\sim\sim\sim p$, there are $2$ pairs of double negation ($\sim$) which cancel out leaving the answer to $\sim p$. If we compare $\sim p$ and $\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim p$, then we can say that they are not equal since $\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim p$ has $6$ pairs of double negations ($\sim$) which cancel out leaving the answer as only $p$. If we compare $\sim p$ and $\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim p$, then we again say that they are not equal, as shown above $\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim\sim p=p$. Thus, $\sim p$ is not equal to $p$.
