Okay I feal so stupid because I cannot figure this out but I am just brain dead and this homework is due in a couple hours so some help would be greatly appreciated...

Note: A real number m is rational iff m=p/q, were p and q are integers and q is not equal to zero.

problem:

Suppose x and y are real numbers, prove or give a counterexample.

a) if x is irrational and y is irrational, then x + y is irrational

b) if x + y is irrational, then x is irrational or y is irrational

c) if x is irrational and y is irrational, then xy is irrational

d) if xy is irrational, then x is irrational or y is irrational.