Suppose A is a subset ofRbounded above and suppose we are given that c "is an element of"R.

Define the sets c + A and cA by c + A = {c + a : a "is an element of" A} and cA = {ca : a "is an element of" A}.

1.) Show that sup(c + A) = c + sup(A)

2.) If c >= 0, show that sup(cA) = c*sup(A)

3.) Postulate a similar statement for sup(cA) for the case where c < 0.