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Consider the statement, "For all integers a and b, if the product of a and b is even, then a is even or b is even." What would be the beginning of a direct proof of this statement? Assume that a is even or b is even. Then a or b = 2k for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. O Assume that ab is even. Then ab = 2k +1 for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. Assume that ab is even. Then ab = 2k for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. O Assume that ab is even. Then ab = 2k for some integer k. We must show that a is even and b is even.

Consider the statement, "For all integers a and b, if the product of a and b is even, then a is even or b is even." What would be the beginning of a direct proof of this statement? Assume that a is even or b is even. Then a or b = 2k for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. O Assume that ab is even. Then ab = 2k +1 for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. Assume that ab is even. Then ab = 2k for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. O Assume that ab is even. Then ab = 2k for some integer k. We must show that a is even and b is even.

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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Discrete Math

Consider the statement, “For all integers a and b, if the product of a and b is even, then a is even or b is even." What would be the beginning of a direct proof of this statement? Assume that a is even or b is even. Then a or b = b is even, so it suffices to show one or the other. 2k for some integer k. We must show that either a is even or Assume that ab is even. Then ab = 2k +1 for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. = 2k for some integer k. We must show that either a is even or b is even, so it Assume that ab is even. Then ab suffices to show one or the other. Assume that ab is even. Then ab 2k for some integer k. We must show that a is even and b is even.
Transcribed Image Text:Consider the statement, “For all integers a and b, if the product of a and b is even, then a is even or b is even." What would be the beginning of a direct proof of this statement? Assume that a is even or b is even. Then a or b = b is even, so it suffices to show one or the other. 2k for some integer k. We must show that either a is even or Assume that ab is even. Then ab = 2k +1 for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other. = 2k for some integer k. We must show that either a is even or b is even, so it Assume that ab is even. Then ab suffices to show one or the other. Assume that ab is even. Then ab 2k for some integer k. We must show that a is even and b is even.
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