$($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.

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$($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 fol$-$

lowing 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.

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