No consider. and .

Assume that "x is irrational or y is irrational" is false. Meaning "x is rational and y is rational" (if you learned logic this is called de'Morgan's law of negation).b) if x + y is irrational, then x is irrational or y is irrational

Then, x+y is rational. A contradiction because x+y is irrational. Thus, this statement is true.

No. Consider and .c) if x is irrational and y is irrational, then xy is irrational

I will leave this as an excerise.d) if xy is irrational, then x is irrational or y is irrational.