Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Statements and Logic
Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.
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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
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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.
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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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