9. Let (G,*) be a group for which H is a subgroup. For any element aɛG. The following set a + H = {a+h | h € H} is called the left coset of H. Prove that, for any distinct elements a,beG, exactly one of the following is true a + H = b+ H or (a+ H) n (b+ H) = Ø).

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Q: Exercise 14. Let G₁ and G₂ be a groups. Then the set G₁ X G₂ is a group with the following binary…

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