Translate the following inference to logic notation: Thomas is bored if and only if it is raining. For all x, x_12 is a janitor if and only if x_12 will write a letter. It is raining if and only if James is writing a letter. James is not a janitor. Therefore Thomas is not bored.
p <-> q. forall x: P(x) <-> Q(x). q <-> Q(a). ~P(a). Therefore ~p.