Let X = {a, b, c} defined by f : X (X such that f = {(a, b), (b, a), (c,c)}. Find the values of f^1, f^2 and f^4.

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Solution:

f = {(a, b), (b, a), (c,c)}

$f^{-1} =\{(b,a), ( a,b), (c,c)\}=f$

We found that $f^{-1}=f$ for given X.

Then, $\\f^2=f(f)=f(f^{-1})=X$

And $\\f^4=[f(f^{-1})]^2=X^2$

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