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Prove the statements. Use only the definitions of the terms and the Assumptions listed below, not any previously established properties of odd and even integers. Follow the directions given in this section for writing proofs of universal statements. Assumptions • In this text we assume a familiarity with the laws of basic algebra, which are listed in Appendix A. • We also use the three properties of equality: For all objects A, B, and C, (1) A = A, (2) if A = B then B = A, and (3) if A = B and B = C, then A = C. • In addition, we assume that there is no integer between 0 and 1 and that the set of all integers is closed under addition, subtraction, and multiplication. This means that sums, differences, and products of integers are integers. • Of course, most quotients of integers are not integers. For example, 3÷2, which equals 3/2, is not an integer, and 3 + 0 is not even a number. Problem: 30. For all integers m, if m is even then 3m + 5 is odd. 1

Prove the statements. Use only the definitions of the terms and the Assumptions listed below, not any previously established properties of odd and even integers. Follow the directions given in this section for writing proofs of universal statements. Assumptions • In this text we assume a familiarity with the laws of basic algebra, which are listed in Appendix A. • We also use the three properties of equality: For all objects A, B, and C, (1) A = A, (2) if A = B then B = A, and (3) if A = B and B = C, then A = C. • In addition, we assume that there is no integer between 0 and 1 and that the set of all integers is closed under addition, subtraction, and multiplication. This means that sums, differences, and products of integers are integers. • Of course, most quotients of integers are not integers. For example, 3÷2, which equals 3/2, is not an integer, and 3 + 0 is not even a number. Problem: 30. For all integers m, if m is even then 3m + 5 is odd. 1

Advanced Engineering Mathematics
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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Prove the statements. Use only the definitions of the terms and the Assumptions listed below, not any previously established properties of odd and even integers. Follow the directions given in this section for writing proofs of universal statements. Assumptions In this text we assume a familiarity with the laws of basic algebra, which are listed in Appendix A. • We also use the three properties of equality: For all objects A, B, and C, (1) A = A, (2) if A = B then B = A, and (3) if A = B and B = C, then A= C. • In addition, we assume that there is no integer between 0 and 1 and that the set of all integers is closed under addition, subtraction, and multiplication. This means that sums, differences, and products of integers are integers. • Of course, most quotients of integers are not integers. For example, 3 ÷ 2, which equals 3/2, is not an integer, and 3 + 0 is not even a number. Problem: 30. For all integers m, if m is even then 3m + 5 is odd.
Transcribed Image Text:Prove the statements. Use only the definitions of the terms and the Assumptions listed below, not any previously established properties of odd and even integers. Follow the directions given in this section for writing proofs of universal statements. Assumptions In this text we assume a familiarity with the laws of basic algebra, which are listed in Appendix A. • We also use the three properties of equality: For all objects A, B, and C, (1) A = A, (2) if A = B then B = A, and (3) if A = B and B = C, then A= C. • In addition, we assume that there is no integer between 0 and 1 and that the set of all integers is closed under addition, subtraction, and multiplication. This means that sums, differences, and products of integers are integers. • Of course, most quotients of integers are not integers. For example, 3 ÷ 2, which equals 3/2, is not an integer, and 3 + 0 is not even a number. Problem: 30. For all integers m, if m is even then 3m + 5 is odd.
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