indirect proof? of that can only use num
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![The method of proof that proves statements in the form 79 →p?
Proof by Contradiction
Direct Proof
Proof by Contraposition
Proof by Cases
QUESTION 2
What is an indirect proof?
A proof that can only use number properties to show that a certain statement is false.
O A proof that assumes a statement's hypothesis is true and uses a series of logic deductions to conclude that the statement's conclusion is true.
A proof that assumes that the statement being proven is false and then attempts to find a contradiction to that assumption proving the original statement to be
true.
A proof that always involves the multiplication of two values.
QUESTION 3
A proof by contraposition relies on p + q being logically equivalent to p → 79
True
False](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff64a74b7-ee4e-4f1b-931f-a071e62b7cb8%2F376010f0-68dd-48d4-a0cf-dfb77b4798e4%2Ft80c4in_processed.png&w=3840&q=75)
Transcribed Image Text:The method of proof that proves statements in the form 79 →p?
Proof by Contradiction
Direct Proof
Proof by Contraposition
Proof by Cases
QUESTION 2
What is an indirect proof?
A proof that can only use number properties to show that a certain statement is false.
O A proof that assumes a statement's hypothesis is true and uses a series of logic deductions to conclude that the statement's conclusion is true.
A proof that assumes that the statement being proven is false and then attempts to find a contradiction to that assumption proving the original statement to be
true.
A proof that always involves the multiplication of two values.
QUESTION 3
A proof by contraposition relies on p + q being logically equivalent to p → 79
True
False
![The method of proof that proves statements in the form p → q?
Direct Proof
Proof by Cases
Proof by Contraposition
O Proof by Contradiction
QUESTION 5
To prove the following statement using a proof by contradiction, what assumption would the proof start with?
Statement: There is an infinite number of prime numbers.
There are no prime number less than 100
There is a finite number of prime numbers
There is an infinite number of prime numbers
There are no even prime numbers
QUESTION 6
If we wanted to prove the following statement using a proof by contradiction, what assumption would we start our proof with?
Statement: When x and y are odd integers, there does not exist an odd integer z such that x + y = z.
When x and y are odd integers, there does not exist an even integer z such that x + y = z.
When x and y are odd integers, there does exist an odd integer z such that x + y = z.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff64a74b7-ee4e-4f1b-931f-a071e62b7cb8%2F376010f0-68dd-48d4-a0cf-dfb77b4798e4%2Fu4cftwp_processed.png&w=3840&q=75)
Transcribed Image Text:The method of proof that proves statements in the form p → q?
Direct Proof
Proof by Cases
Proof by Contraposition
O Proof by Contradiction
QUESTION 5
To prove the following statement using a proof by contradiction, what assumption would the proof start with?
Statement: There is an infinite number of prime numbers.
There are no prime number less than 100
There is a finite number of prime numbers
There is an infinite number of prime numbers
There are no even prime numbers
QUESTION 6
If we wanted to prove the following statement using a proof by contradiction, what assumption would we start our proof with?
Statement: When x and y are odd integers, there does not exist an odd integer z such that x + y = z.
When x and y are odd integers, there does not exist an even integer z such that x + y = z.
When x and y are odd integers, there does exist an odd integer z such that x + y = z.
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