Problem 5. Order 9 of the following sentences so that they form a logical proof by contradiction of the statement: If the square of an integer is odd then the original integer is also odd. • Suppose n is an integer such that n² is even. • Therefore, n is odd • Ek € Z such that n = 2k+ 1. • Ek € Z such that n = 2k. • 3j € Z such that n² = 2 j • Presume that the given statement is incorrect. • Suppose n is odd. • n² = 4k² • Suppose n is even. • Son² is odd and n² is even. • Let n € Z such that n² is odd. • n² is even
Problem 5. Order 9 of the following sentences so that they form a logical proof by contradiction of the statement: If the square of an integer is odd then the original integer is also odd. • Suppose n is an integer such that n² is even. • Therefore, n is odd • Ek € Z such that n = 2k+ 1. • Ek € Z such that n = 2k. • 3j € Z such that n² = 2 j • Presume that the given statement is incorrect. • Suppose n is odd. • n² = 4k² • Suppose n is even. • Son² is odd and n² is even. • Let n € Z such that n² is odd. • n² is even
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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Transcribed Image Text:Problem 5.
Order 9 of the following sentences so that they form a logical
proof by contradiction of the statement:
If the square of an integer is odd then the original integer is also
odd.
• Suppose n is an integer such that n² is even.
• Therefore, n is odd
• Ek € Z such that n = 2k+ 1.
• Ek € Z such that n = 2k.
• 3j € Z such that n² = 2 j
• Presume that the given statement is incorrect.
• Suppose n is odd.
• n² = 4k²
• Suppose n is even.
• Son² is odd and n² is even.
• Let n € Z such that n² is odd.
• n² is even
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