Answer to Question #238987 in Discrete Mathematics for Joseph

Question

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. 

Answer 1

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