Let A and B be non-empty bounded subsets of R. DefineA − B := {a − b : a ∈ A, b ∈ B}.Prove thatsup(A − B) = sup A − inf B

Step 1: Define the sets

Let A and B be non-empty bounded subsets of R. We define A - B as the set of all differences a - b, where a is an element of A and b is an element of B.

Step 2: Show that sup(A - B) is an upper bound for A - B

We know that for any a in A and b in B, a - b is less than or e Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.