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

$($a$)$ Show that $\text{'}$ not $\text{'}$ and $\text{'}^\text{'}$ form a functionally complete collection of logical operators.

$\%$

$(2$ marks$)$

$($b$)$ Let $C(x),D(x),$ and $E(x)$ be the statements $"x$ is a contractor," $"x$ is dependable," and $"x$ is an engineer," respectively. Express each of the following statements using quantifiers, logical connectives, and $C(x),S(x),$ and $E(x).$

$($i$)$ No contractors are dependable.

$($ii$)$ Some contractors are engineers.

$($iii$)$ Some engineers are not dependable.

Does $($iii$)$ follow from $($i$)$ and $($ii$)?$ Justify your answer. $\%$

$(3$ marks$)$