Answer Happy

Let A and B be non-empty sets with A ⊆ B, and assume B is
bounded.
a) Prove that inf(B) ≤ inf(A) ≤ sup(A) ≤ sup(B).
b) Prove or disprove: There exists some A,B with A 􏰀 B (i.e. A
is a subset of B but NOT equal to B) where all of the above
inequalities are tight (i.e. they can all be equal).
Let A and B be non-empty sets with A CB, and assume B is bounded. 7 (a) Prove that inf(B) < inf(A) < sup(A) < sup(B). (b) Prove or disprove: There exists some A, B with A Ç B (i.e. A is a subset of B but NOT equal to B) where all of the above inequalities are tight (i.e. they can all be equal).