Q5 (6 points) Suppose A, B CR are non-empty subsets. a) Prove that if A is...

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Q5 (6 points) Suppose A, B CR are non-empty subsets. a) Prove that if A is bounded above, and A > 0, then the subset XA = {Aa| a € A} is bounded above, and satisfies sup(AA) = Asup(A). b) Prove that if A is bounded above, then -A = {-a| a € A} is bounded below, and inf(-A) = – sup(A). c) Prove that if A, B are bounded above, then so is the subset A + B = {a + b| a E A, b e B}, and sup(A + B) = sup(A) + sup(B). Q5 (6 points) Suppose A, B CR are non-empty subsets. a) Prove that if A is bounded above, and A > 0, then the subset XA = {Aa| a € A} is bounded above, and satisfies sup(AA) = Asup(A). b) Prove that if A is bounded above, then -A = {-a| a € A} is bounded below, and inf(-A) = – sup(A). c) Prove that if A, B are bounded above, then so is the subset A + B = {a + b| a E A, b e B}, and sup(A + B) = sup(A) + sup(B).