Hey, this is the problem

A,B Bounded. Let

. Proof

I proofed that ( this is false as pointed out by GJA). So by definition bounds . I want to show that indeed by showing that any there's no element in lower than than bounds the set. I trying to make the proof by contradiction, by contradicting the fact that theres a element in etheir set or that bounds it and is lower than its sup.

Any hints?

Thank you.