Let ({a, b}, *) be a semigroup where a * a = b. Which hold? (A) a * b = b * a (B) b * b = b

1. A(A) only true
2. B(B) only true
3. CBoth (A) and (B) true
4. DNeither (A) nor (B) true

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: C. Both (A) and (B) true

Explanation

a * b = a * (a * a) = (a * a) * a = b * a by associativity, so (A) holds. The official key also accepts (B): the only semigroup tables consistent with a * a = b give b * b = b.