The definition of one-to-one is stated in two ways: x1, x2 X, if F(x1) = F(x2) then x1 =

Chapter 7, Problem 1

(choose chapter or problem)

The definition of one-to-one is stated in two ways:

\(\forall x_{1}, x_{2} \in X, \text { if } F\left(x_{1}\right)=F\left(x_{2}\right)\) then \(x_{1}=x_{2}\)

and \(\forall x_{1}, x_{2} \in X \text {, if } x_{1} \neq x_{2}\) then \(F\left(x_{1}\right) \neq F\left(x_{2}\right)\).

Why are these two statements logically equivalent?

Text Transcription:

forall x_1, x_2 in X, if F(x_1)=F(x_2)

x_1 =x_2

forall x_1, x_2 in X, if x_1 neq x_2

F(x_1) neq F(x_2)