Question #308432

the set of all functions of {1 2 3...,10} to itself forms a group w.r.t the composition of function.true or false


1
Expert's answer
2022-03-10T03:08:56-0500

Consider the function

f:{1,2,3,...,10}{1,2,3,...,10},f:\{1, 2 ,3,...,10\}\to\{1 ,2, 3,...,10\},

f(x)=1.f(x)=1.

This function is not a bijection, and hence is not invertible. Therefore, ff has no inverse, and we conclude that the set of all such functions does not form a group with respect to the operation of composition.



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