1. Let S be the subset of Q given by S = Here, Q is the set of all rational numbers. (a) Show that the following binary operation * on S is well defined: a * b = a +b+ 5ab (a, b e S) (b) Prove that the binary structure (S, *) is a group.

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Q: Let (G, ) be a group. Define a new binary operation * on G by the formula a * b = b · a for all a, b…

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