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

$($a$)$ Using truth table method, show that the hypotheses "Alice is not elected class president or Carol is elected treasurer" and "Carol is not elected treasurer" imply the conclusion "Alice is not elected class president." $\%$

$($b$)$ Using symbols and theory of inference, show that the hypotheses $"$If I am lucky, then I am employed", $"$If I am employed or clever, then I am rich" and "I am lucky" imply the conclusion "I am rich."

$\%$

$(3$ marks$)$