Logic question Help Please!?

Question

Find a compound proposition involving the propositions p, q, and r that is true when p and q are true and r is false, but that is false otherwise

Answer 1

Define

p -- x <>0
q -- y <>0
r -- z = 0. x, y and z real numbers.

Compound proposition: If x<>0 (p), y <> 0 (q) and z<>0 (not r), then x * y * z <> 0

If p is false or if q is false or if r is true, then at least one of the numbers x, y, z is 0, so that their product is 0 and the compound proposition becomes false.

Answer 2

p and q and (not r)

Answer 3

and(and(p,q),not(r))