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Consider the following statement: For all integers a and b, if a is even and b is a multiple of 6, then ab is a multiple of 12. a. Prove the statement by choosing the appropriate steps in the correct order. Ⓒab 2k-6j a = 2k, k € Z and b = 6j, j = Z 2k, k € Z and b = 18j, j = Z 2k. 18j a = Ⓒab Ⓒab = multiple of 6. = = 12(kj) - Let a be an arbitrary even integer and let b be an arbitrary integer which is a Therefore, ab is a multiple of 12.

Consider the following statement: For all integers a and b, if a is even and b is a multiple of 6, then ab is a multiple of 12. a. Prove the statement by choosing the appropriate steps in the correct order. Ⓒab 2k-6j a = 2k, k € Z and b = 6j, j = Z 2k, k € Z and b = 18j, j = Z 2k. 18j a = Ⓒab Ⓒab = multiple of 6. = = 12(kj) - Let a be an arbitrary even integer and let b be an arbitrary integer which is a Therefore, ab is a multiple of 12.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following statement: For all integers \(a\) and \(b\), if \(a\) is even and \(b\) is a multiple of 6, then \(ab\) is a multiple of 12. a. Prove the statement by choosing the appropriate steps in the correct order. 1. Let \(a\) be an arbitrary even integer and let \(b\) be an arbitrary integer which is a multiple of 6. 2. \(a = 2k, \, k \in \mathbb{Z}\) and \(b = 6j, \, j \in \mathbb{Z}\) 3. \(ab = 2k \cdot 6j\) 4. \(ab = 12(kj)\) 5. Therefore, \(ab\) is a multiple of 12.
Transcribed Image Text:Consider the following statement: For all integers \(a\) and \(b\), if \(a\) is even and \(b\) is a multiple of 6, then \(ab\) is a multiple of 12. a. Prove the statement by choosing the appropriate steps in the correct order. 1. Let \(a\) be an arbitrary even integer and let \(b\) be an arbitrary integer which is a multiple of 6. 2. \(a = 2k, \, k \in \mathbb{Z}\) and \(b = 6j, \, j \in \mathbb{Z}\) 3. \(ab = 2k \cdot 6j\) 4. \(ab = 12(kj)\) 5. Therefore, \(ab\) is a multiple of 12.
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