Condition of semigroup homomorphism should be ____________(a) f(x * x) = f(x * y)(b) f(x) = f(y)(c) f(x) * f(y) = f(y)(d) f(x * y) = f(x) * f(y)I had been asked this question in my homework.I'm obligated to ask this question of Group Axioms in division Groups of Discrete Mathematics

Condition of semigroup homomorphism should be ____________(a) f(x * x)

1.	Condition of semigroup homomorphism should be ____________(a) f(x * x) = f(x * y)(b) f(x) = f(y)(c) f(x) * f(y) = f(y)(d) f(x * y) = f(x) * f(y)I had been asked this question in my homework.I'm obligated to ask this question of Group Axioms in division Groups of Discrete Mathematics
Answer» The correct option is (d) F(x * y) = f(x) * f(y) For explanation I would say: Consider two semigroups (S,∗) and (S’,∗’). A FUNCTION f: S -> S’ is CALLED a semigroup homomorphism if f(a∗b) = f(a)∗f(b). Suppose f is also one-to-one and onto. Then f is called an isomorphism between S and S’ and S and S’ are SAID to be isomorphic semigroups.

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Condition of semigroup homomorphism should be ____________(a) f(x * x) = f(x * y)(b) f(x) = f(y)(c) f(x) * f(y) = f(y)(d) f(x * y) = f(x) * f(y)I had been asked this question in my homework.I'm obligated to ask this question of Group Axioms in division Groups of Discrete Mathematics

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