Translate the following inference to logic notation: If Robert cooks, then Thomas is making tea. If Joseph were a janitor, then Thomas is making tea. For all x, y will not cook. If Michael were a cashier, then Joseph is a janitor. If Thomas makes tea, then Robert is cooking. Therefore Michael is not a cashier.
P(a) -> p. q -> p. forall x: ~P(x). r -> q. p -> P(a). Therefore ~r.