Problem 6. Order 7 of the following sentences so that they form a logical proof by contrapositive of the statement: VxEZ, 9x + 15 even ⇒ x is odd • 9x+15=2(9k+7)+1 x is even. • Suppose x is an integer that is not odd. • Then a miracle occurred. • 9x + 15 is even • 9x+15= 9(2k) + 15 = 18k+14+1 • Ek such that x = 2k • 9x + 15 is odd • 9x+15=2j+1 for some integer j • Suppose 9x + 15 is not even.
Problem 6. Order 7 of the following sentences so that they form a logical proof by contrapositive of the statement: VxEZ, 9x + 15 even ⇒ x is odd • 9x+15=2(9k+7)+1 x is even. • Suppose x is an integer that is not odd. • Then a miracle occurred. • 9x + 15 is even • 9x+15= 9(2k) + 15 = 18k+14+1 • Ek such that x = 2k • 9x + 15 is odd • 9x+15=2j+1 for some integer j • Suppose 9x + 15 is not even.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Problem 6.
Order 7 of the following sentences so that they form a logical
proof by contrapositive of the statement:
VxEZ, 9x + 15 even ⇒ x is odd
• 9x+15=2(9k+7)+1
x is even.
• Suppose x is an integer that is not odd.
• Then a miracle occurred.
• 9x + 15 is even
• 9x+15= 9(2k) + 15 = 18k+14+1
• Ek such that x = 2k
• 9x + 15 is odd
• 9x+15=2j+1 for some integer j
• Suppose 9x + 15 is not even.
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