Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN: 9781305658004
Author: Ron Larson
Publisher: Cengage Learning
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Chapter A, Problem 16E
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If n is an odd integer, then n2 is also an odd integer.
Chapter A Solutions
Elementary Linear Algebra (MindTap Course List)
Ch. A - Using Mathematical Induction In Exercises 1-4, use...Ch. A - Prob. 2ECh. A - Prob. 3ECh. A - Prob. 4ECh. A - Prob. 5ECh. A - Prob. 6ECh. A - Prob. 7ECh. A - Prob. 8ECh. A - Prob. 9ECh. A - Prob. 10E
Ch. A - Prob. 11ECh. A - Prob. 12ECh. A - Prob. 13ECh. A - Prob. 14ECh. A - Using Proof by Contradiction In Exercises 1526,...Ch. A - Prob. 16ECh. A - Prob. 17ECh. A - Prob. 18ECh. A - Prob. 19ECh. A - Prob. 20ECh. A - Prob. 21ECh. A - Prob. 22ECh. A - Prob. 23ECh. A - Prob. 24ECh. A - Prob. 25ECh. A - Prob. 26ECh. A - Prob. 27ECh. A - Prob. 28ECh. A - Prob. 29ECh. A - Prob. 30ECh. A - Prob. 31ECh. A - Prob. 32ECh. A - Prob. 33E
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- Using Proof by Contradiction In Exercises 1526, use proof by contradiction to prove the statement. If p is an integer and p2 is odd, then p is odd. Hint: An odd number can be written as 2n+1, where n is an integer.arrow_forwardDetermine if the statement is true or false. If the statement is false, then correct it and make it true. 3n3n+1 is true for all natural numbers n greater than 2.arrow_forwardProve using proof of contradiction. Include explanation. If n is an odd integer, then n2 is also an odd integer.arrow_forward
- Prove using proof of contradiction. Include explanation. If n is an even integer, then 7n + 4 is an even integer.arrow_forwardProve using contrapositive proof. Include explanation. If n is an odd integer, then n2 is also an odd integer.arrow_forwardUsing direct, indirect and contradiction 1. Prove that if n is a positive integer, then n is odd if and only if 5n + 6 is odd.arrow_forward
- number theoryarrow_forwardUsing indirect or direct proof methods, prove for every positive integer n, n2 + 6n + 5 is not prime.arrow_forwardTheorem: If a and b are consecutive integers, then the Choose a match sum a + b is odd. Proof: Assume that a and b are consecutive integers. Because Proof by Contradiction a and b are consecutive we know that b = a + 1. Thus, the sum a +b may be re-written as 2a + 1. Thus, there exists a number k such that a + b = 2k + 1 so the sum a + Proof by Contrapositive b is odd. O Direct Proof Theorem: If a and b are consecutive integers, then the sum a + b is odd. Proof: Assume that a and b are consecutive integers. Assume also that the sum a + b is not odd. Because the sum a + b is not odd, there exists no number k such that a + b = 2k + 1. However, the integers a and b are consecutive, so we may write the sum a + b as 2a + 1. Thus, we have derived that a+ b k+1 for any integer k and also that a + b = 20 + 1. If we hold that a and b are consecutive then we know that the sum a + b must be odd.arrow_forward
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