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Question: a set c of real numbers is convex if and...

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A set C of real numbers is convex if and only if for all elements in x, y ∈ C and for every real numbers t with 0 ≤ t ≤ 1, tx + (1 − t)y ∈ C. Suppose a, b ∈ R. Show that the set C = {x ∈ R | ax ≤ b} is convex.

I am not sure how to do the contrapositive, contradiction, or the direct proof for this. Thank you!

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