Translate the following inference to logic notation: It is sunny if and only if Mary is writing a letter. Mary is not a carpenter. For all x, x_23 will not write a letter. Mary is a carpenter if and only if it is windy. Therefore it is not sunny and it is not windy.
p <-> P(a). ~q. forall x: ~P(x). q <-> r. Therefore ~p and ~r.