Let (G, ○) be an arbitrary group with at least two elements. Which of the following statements is not true? (a) For every pair of elements a, b ∈ G, the element a ○ b also belongs to the set G. (b) For every element a ∈ G, there exists an element b ∈ G such that b ○ a = b. (c) If for some elements a, b, c ∈ G it holds that a ○ b = c, then b = c. (d) If e ∈ G is the neutral element, then for every element a ∈ G, there exists an element b ∈ G such that a ○ b = e. (e) If e ∈ G is the left-neutral element and f ∈ G is the right-neutral element, then e = f

Let (G, ○) be an arbitrary group with at least two elements. Which of the following statements is not true? (a) For every pair of elements a, b ∈ G, the element a ○ b also belongs to the set G. (b) For every element a ∈ G, there exists an element b ∈ G such that b ○ a = b. (c) If for some elements a, b, c ∈ G it holds that a ○ b = c, then b = c. (d) If e ∈ G is the neutral element, then for every element a ∈ G, there exists an element b ∈ G such that a ○ b = e. (e) If e ∈ G is the left-neutral element and f ∈ G is the right-neutral element, then e = f

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 37E: Let H and K be arbitrary groups and let HK denotes the Cartesian product of H and K: HK=(h,k)hHandkK...

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