Translate the following inference to logic notation: For all x, y is a mechanic if and only if y will make tea. There is at least one x for which y will make tea if and only if y is a mechanic. Therefore there is at least one x for which y will make tea if and only if y is a mechanic.
forall x: P(x) <-> Q(x). exists x: Q(x) <-> P(x). Therefore exists x: Q(x) <-> P(x).