find one counterexample to show that each conjecture is false.?

Question

1. the product of two positive numbers is greater than either number
2. the quotient of two prpoer fractions is a proper fraction.

Answer 1

For the first, 1 times any number is the number itself, say 1x=x but x is not greater than x, since x=x.

For the second say 1/2 divided by 1/15 which gives 15/2 and it is not a propper fraction.

Answer 2

1)

1/2 * 1/2 = 1/4

1/4 < 1/2

2) (1/2) / (1/2) = 1. 1 is not a proper fraction.