Solution for QID #97407: Let A and B be a bounded set. sup(A union B)=max{sup A, s | StudyHelpMe

Let A and B be a  bounded set. sup(A union B)=max{sup A, sup  B) I am struggling with the proof Let x belongs to A to B, then x belongs to A or x belongs to B x<= sup A, x<= sup B It means x<=max(sup A, sup B) i am struggling with the next step when x<=max(sup A, sup B) implies sup(AUB)<=max (sup A, sup B) I know that x<=sup(AUB), but I don't know why sup (A U B )<= max (Sup A, sup  B)