1(a) If , and , then .

(b) If , and , then .

(c) If , and , then .

(d) If , then .

Axioms

(1) If and , then their product is in .

(2) , for all .

(3) for all .

(4) contains an element , such that for every .

(5) If and , then there exists an element such that .

So (c) and (d) follows from Axiom (5), and (b) follows from Axiom (2). How about (a)?