   Chapter 7.2, Problem 1ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# The definition of onr-to-one is stated in two ways: ∀ x 1 , x 2 ∈ X ,   if  F ( x 1 ) = F ( x 2 ) then  x 1 = x 2 and   ∀ x 1 , x 2 ∈ X   if   x 1 ∉ x 2     then   F ( x 1 ) ≠ F ( x 2 ) . Why are these two statements logocally equivalent?

To determine

To find:

The reason for logically equivalence between two given definitions of one-to-one.

Explanation

Given information:

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

x1,x2X, if F(x1)=F(x2) then x1=x2 and x1,x2X, if x1x2then F(x1)F(x2).

Concept used:

pqqp.

Calculation:

The statement pq is called implication.

It is logically equivalent to its contrapositive statement.

i.e

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