Translate the following inference to logic notation: If Thomas were a lawyer, then Barbara is cooking. Barbara is a mechanic if and only if Thomas is a lawyer. For all x, if x_17 cooks, then x_17 is a mechanic. Therefore if Barbara cooks, then Thomas is a lawyer.
p -> P(a). Q(a) <-> p. forall x: P(x) -> Q(x). Therefore P(a) -> p.