1. For all numbers (y), y • 2. If x is a whole number, then Vx is also a whole number. 3. All numbers that end in 1 are prime numbers.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 4TFE: Label each of the following statement as either true or false. only if
icon
Related questions
Question
100%
B. Prove or disprove the following statements using counterexample.
1
1. For all numbers (y), y <
y
2. If x is a whole number, then x² is also a whole number.
3. All numbers that end in 1 are prime numbers.
4. For any angle, there exists a complementary angle.
5. All equations have integer solutions.
6. The sum of any two whole numbers is divisible by 2.
7. Every whole number greater than five is the sum of either two or three
consecutive whole numbers.
8. Every whole number between 25 and 50 is the product of two whole
numbers greater than 1.
9. If the product of two natural numbers is an even natural number, then
the two natural numbers are even natural numbers.
10. The sum of five consecutive prime numbers is even.
Transcribed Image Text:B. Prove or disprove the following statements using counterexample. 1 1. For all numbers (y), y < y 2. If x is a whole number, then x² is also a whole number. 3. All numbers that end in 1 are prime numbers. 4. For any angle, there exists a complementary angle. 5. All equations have integer solutions. 6. The sum of any two whole numbers is divisible by 2. 7. Every whole number greater than five is the sum of either two or three consecutive whole numbers. 8. Every whole number between 25 and 50 is the product of two whole numbers greater than 1. 9. If the product of two natural numbers is an even natural number, then the two natural numbers are even natural numbers. 10. The sum of five consecutive prime numbers is even.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning