Mathematics · Abstract Algebra
Let A be a non-empty set and S be the set of all functions from A to A. Let * be a binary operation on S defined by (f * g)(x) = f(g(x)) for all x ∈ A. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1* is not a binary operation on S
- 2(S, *) is a group
- 3(S, *) is a semigroup but not necessarily a group✓
- 4(S, ) does not contain an identity element
Correct answer
(S, *) is a semigroup but not necessarily a group
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