3. Suppose A and B are non-empty sets of real numbers that are both bounded above....

3. Suppose A and B are non-empty sets of real numbers that are both bounded above.

(a) Prove that, if A ⊆ B, then supA ≤ supB.

(b) Prove that supA∪B = max{supA,supB}.

(c) Prove that, if A∩B 6= ∅, then supA∩B ≤ min{supA,supB}. Give an example to show that equality need not hold.

Expert Solution

Colby Messinger answered 1 year ago

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