Condition of semigroup homomorphism should be ____________ans.f(x * y) = f(x) * f(y)f(x) = f(y)f(x * x) = f(x * y)f(x) * f(y) = f(y) Previous Marked for Review Next
Question
Condition of semigroup homomorphism should be ____________ans.f(x * y) = f(x) * f(y)f(x) = f(y)f(x * x) = f(x * y)f(x) * f(y) = f(y) Previous Marked for Review Next
Solution
The condition for a semigroup homomorphism should be f(x * y) = f(x) * f(y). This means that the function f preserves the operation * under which the semigroup is defined. If x and y are elements of the semigroup, then the operation * applied to f(x) and f(y) should give the same result as applying f to the result of the operation * applied to x and y.
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