Thread: Using supremum and infimum

can anybody help me solve the following parts of a proposition?

prove If x < 0, then sup(xA) = x(inf A).

and If x < 0, then inf(xA) = x(sup A)

thanks!

Is it know that A is bounded?

For the first, assume that a = inf A. Write the two statements this means by definition. Then write the two statements it takes to prove that xa is sup (xA). If it is not clear how to proceed further, post the results.