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Opinion on proof (cartesian product -sets)-some guidance needed

Good day to all

I have attached the question asked and my work for better legibility. I need to prove that the LHS is a proper subset of the RHS. I have (I believe) managed to proved that it is a subset of the RHS but not a proper subset. I know that to do so, I would need to prove that the LHS subset of RHS and LHS different than RHS. This is where my problem arises. Any help would be greatly appreciated.

Kindest regards