Let ({a, b}, *) be a semigroup where a * a = b. Consider:
(A) a * b = b * a
(B) b * b = b
Choose the most appropriate answer from the options given below:
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Correct answer: C. Both (A) and (B) true
Explanation
a*b = a*(a*a) = (a*a)*a = b*a by associativity. a³ is a or b. If a³ = a then b*b = a⁴ = a² = b; if a³ = b then b*b = a⁴ = a*a³ = a*b = a³ = b. So b*b = b in every case.More Discrete Structures and Optimization questions
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