Mathematics · Abstract Algebra
Let (S, *) be a semigroup. Furthermore, for every x and y in S, if x ≠ y, then x * y ≠ y * x. Based on the defined semigroup, choose the correct equalities from the options given below: I. For every x in S, x * x = x II. For every x, y in S, x * y * x = x III. For every x, y, z in S, x * y * z = x * z
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Only I and II are correct
- 2Only II and III are correct
- 3All I, II, and III are correct✓
- 4Only I and III are correct
Correct answer
All I, II, and III are correct
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