Suppose p is an upper bound for S. Then for all y in S. What can you say about y+ S?

This last statement is clearly untrue. Do you really have that "sup(S)" in the middle?b) Prove that x + sup(S) is an upper bound of x + S. Conclude that the sup(x+ S) ≤ x + sup(S)

C) Prove that x + sup(S) = sup(S) = sup(x+S)

Thanks for any help provided.