Answers:

1. We need to find real numbers a and b such that b² > a² and b < a (b is not greater than a).

Counterexample : Let a = 3 and b = -4. Then a² = 3² = 9 and b² = (-4)² = 16, and so b² > a² .

But b < a since -4 < 3.

2. We need to find real numbers x, y and z such that x > y and xz < yz (xz is not greater than yz).

Counterexample : Let x = 10, y = 8 and z = -3. Then x > y, since 10 > 8. But xz = 10 * (-3) = -30

and yz = 8 * (-3) = -24.

-30 < -24, and hence xz < yz.