Disprove each of these existence statements by proving that its negation is true.  a) There exists some natural number n such that n2+7n+12 is a prime number. b) There exists positive integers m and n such that m2+n2=11

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 27E: Prove that the least common multiple of two nonzero integers exists and is unique.
icon
Related questions
Topic Video
Question
100%

Disprove each of these existence statements by proving that its negation is true. 

a) There exists some natural number n such that n2+7n+12 is a prime number.

b) There exists positive integers m and n such that m2+n2=11.

Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,