$($Answer must be in your own hand$-$writing$)$

$($a$)$ Let $p$ and $q$ be the statements "I stay up late" and "I sleep until noon" Symbolize the statement $"$If I sleep until noon, then it is not necessary that I stay up late." $\%$

$($b$)$ Construct truth table for $(po+$notq$)harrnot(po+q).$

$(1$ mark$)\%$

$($c$)$ Test whether $(pharrnotq)$ is logically equivalent to $(p$notq${)}^{{?}^{?}}(notpq)\%$

$(2$ marks$)$