Okay, I have this problem from a maths textbook and its along the same lines as

If S and T are sets

the Cartesian product S x T of S and T is defined

[(s,t) : s ∈ S, t ∈ T}

Prove if S and T are convex sets in ℝ^n and ℝ^m

then ℝ^(n+m) is convex also

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I have the answer but I'm completely confused on how it was derived