Translate the following inference to logic notation: It is raining and Mary is taking a plane. For all x, if x_23 writes a letter, then x_23 is working. If Charles were happy, then Michael is working. Michael is writing a letter or Charles is happy. Therefore it is raining and Michael is working.
p and q. forall x: P(x) -> Q(x). r -> Q(a). P(a) or r. Therefore p and Q(a).