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Determine whether the statement is true or false. If it is​ true, give two examples to illustrate it. If it is​ false, give a single counterexample.   If a<​b, then a2

Determine whether the statement is true or false. If it is​ true, give two examples to illustrate it. If it is​ false, give a single counterexample.   If a<​b, then a2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Determine whether the statement is true or false. If it is​ true, give two examples to illustrate it. If it is​ false, give a single counterexample.
 
If
a<​b,
then
a2<b2.
 
 
 
Choose the correct answer below.
 
 
A.
The statement is false. If
a=3
and
b=−​2,
then
a<b
but
a2=9
is not less than
b2=​4,
which is a counterexample.
 
B.
The statement is true. If
a=2
and
b=​3,
then
a<b
and
a2=4
is less than
b2=9.
If
a=0
and
b=​2,
then
a<b
and
a2=0
is less than
b2=4.
 
C.
The statement is false. If
a=−3
and
b=−​2,
then
a<b
but
a2=9
is not less than
b2=​4,
which is a counterexample.
 
D.
The statement is true. If
a=−3
and
b=​2,
then
a<b
and
a2=−9
is less than
b2=4.
If
a=−1
and
b=​1,
then
a<b
and
a2=−1
is less than
b2=1.
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