Which of following statements are correct regarding supremums and infimums?

Question

1. A finite, non empty set always contains its supremum

Correct as in a finite set no elements are same and some element is highest

2. If $a < L , \forall a \in A$ then Sup A < L

Incorrect. Example take (1,8]. Here L= SupA =8

3. If A and B are sets with property that $a <b \forall a \in A$ and every $b\in B$, then Sup A < Inf B

Incorrect. A= (1,2) B= [2,5)

4. If sup A = s and Sup B = t then Sup (A + B) = t +s

Correct

5. If Sup A $\leq$ Sup B, then $\exists b \in B$ such that it is upper bound for A

Incorrect. A= (2,6) B =(4,6)

Are these correct ? Please and Thanks