Problem 2. Order 8 of the following sentences so that they form a logical proof by contrapositive of the statement: If the sum of two integers is even then they have the same parity. • Without loss of generality assume x is even and y is odd. • Suppose x and y are integers with opposite parity. • x+y=2k+2j+1 • x+y is odd
Problem 2. Order 8 of the following sentences so that they form a logical proof by contrapositive of the statement: If the sum of two integers is even then they have the same parity. • Without loss of generality assume x is even and y is odd. • Suppose x and y are integers with opposite parity. • x+y=2k+2j+1 • x+y is odd
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 2.
Order 8 of the following sentences so that they form a logical
proof by contrapositive of the statement:
If the sum of two integers is even then they have the same parity.
• Without loss of generality assume x is even and y is odd.
• Suppose x and y are integers with opposite parity.
x+y=2k+2j+1
•
• x+y is odd
• Es such that x+y=2s +1
• Assume x+y even implies x and y have the same parity.
• Therefore, x+y is even ⇒ x and y have the same parity.
• Ek, j€ Z such that x = 2k and y=2j+1
• Either x is odd and y is even or x is even and y is odd.
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