Originally Posted by

**esuahcdss12**
I just started to learn this subject and I got how to prove and to find infimum and supremum. But I'm having difficulty with the following question (I have no idea where to start or how to do the proof). This is the question:

Given two bounded sets, X and Y, such that all of their element are non-negative real numbers, define the set X*Y as follows:

. . . . .X*Y = {x*y : x is an element of X, y is an element of Y}

Prove the following:

. . .a) inf{X*Y} = inf X * inf Y

. . .b)sup{X*Y} = supX * supY

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