posted by dgibson on .
If we multiply "a" and "b",when will:
a. the product be larger than both "a" and "b"?
b. the Product be less than "a"?
c. the product be less than "b"?
d. the product be less than"a" and "b"?
e. the product be greater than "a"?
f. the product be greater than "b"?
g. the product be greater than "a" and "b"?
h. the product be equal to either "a" and "b"?
i. the product be zero?
I suppose what you mean by "If we multiply "a" and "b..." is the product ab of a and b.
a) We want a<ab and b<ab
Consider when they have the same sign or different signs. If a and b are pos., then both a>1 and b>1
If both are neg., then a<ab and b<ab hold for all a,b negative.
If they have different signs then
a<ab or b<ab will not hold for one of them because ab<0 but one is greater than 0. Therefore the empty set with different signs.
All of the rest are along the same lines, except i). They can both be 0, but at least one of a,b must be 0.
Show some work so we can see where the difficulties are. I don't see how it helps if I do all of them. There are a lot of cases to consider, so you need to check your work carefully.