   Chapter 7.4, Problem 10ES ### 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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# In 10-14 s denotes the sets of real numbers strictly between 0 and 1. That is S = { x ∈ R|0< x < 1 } Let U = { x ∈ R|0< x < 2 } . Prove that S and U have the same cardinality.

To determine

To show:

S and U have the same cardinality.

Explanation

Given information:

S={xR:0<x<1}U={xR:0<x<2}

Concept used:

A function is said to be one-to-one function if distinct elements in domain must be mapped with distinct elements in codomain.

A function is onto function if each element in codomain is mapped with at least one element in domain.

Proof:

Consider f:SU by f(x)=2x,xR such that 0<x<1.

To show: f is one-to-one.

Let f(x)=f(y)

2x=2yx=y

f is one-to-one

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