Let A and B be two nonempty bounded sets of real numbers. Let C={ab:a∈A,b∈B}. Show that C is a bounded set and that sup(C)=sup(A)⋅sup(B) and inf(C)=inf(A)⋅inf(B).
a) C is unbounded, and the supremum and infimum cannot be determined.
b) C is sup(C)=sup(A)+sup(B) and inf(C)=inf(A)+inf(B).
c) C is sup(C)=sup(A)⋅sup(B) and inf(C)=inf(A)⋅inf(B).
d) C is unbounded, and the supremum and infimum are equal.