Translate the following inference to logic notation: For all x, z will work if and only if z is a carpenter. Michael is playing a game if and only if Linda is making tea. Linda is a carpenter if and only if Michael is playing a game. For all x, z will not work. Therefore Linda is not making tea.
forall x: P(x) <-> Q(x). p <-> q. Q(a) <-> p. forall x: ~P(x). Therefore ~q.