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Challenge Yourself #CHAPTER4

Two groups are isomorphic if and only if __________ is existed between them.
Homomorphism
Endomorphism
Isomorphism
Condition of semigroup homomorphism should be ____________.
F(x * x) = f(x * y)
F(x) = f(y)
F(x) * f(y) = f(y)
F(x * y) = f(x) * f(y)
A function f:(M,∗)→(N,×) is a homomorphism if ______.
F(a, b) = a*b
f(a, b) = a/b
F(a, b) = f(a)+f(b)
F(a, b) = f(a)*f(a)
A function defined by f(x)=2*x such that f(x+y)=2x+y under the group of real numbers, then ________.
Isomorphism exists
Homomorphism exists
Association exists
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