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For the following proof, determine which of the statements given below is being proved. Proof. Assume a and b are odd integers. Then a = 2k + 1 and b = 21+1 for some k,lEZ. Then ab? = (2k + 1)(2/+ 1)² = 8k/² + 8kl+ 2k + 412 + 41+ 1=2(4k/² + 4kl + k +21? +21) + 1. Since 4kl? + 4kl+k +21? +21€Z, we see ab² is odd. А. None of the above. В. If a or b is even, then ab is even. "If ab² is even, then a is even or b is even. D. O D'If a and b are even, then ab is even. O E. If ab is even, then a and b are even.

For the following proof, determine which of the statements given below is being proved. Proof. Assume a and b are odd integers. Then a = 2k + 1 and b = 21+1 for some k,lEZ. Then ab? = (2k + 1)(2/+ 1)² = 8k/² + 8kl+ 2k + 412 + 41+ 1=2(4k/² + 4kl + k +21? +21) + 1. Since 4kl? + 4kl+k +21? +21€Z, we see ab² is odd. А. None of the above. В. If a or b is even, then ab is even. "If ab² is even, then a is even or b is even. D. O D'If a and b are even, then ab is even. O E. If ab is even, then a and b are 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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For the following proof, determine which of the statements given below is being proved. Proof. Assume a and b are odd integers. Then a = 2k + 1 and b = 21+1 for some k,lEZ. Then ab? = (2k + 1)(2/+ 1)2 = 8k/² + 8kl + 2k + 412 + 41+ 1=2(4kl? + 4kl + k +212 +21) + 1. Since 4kl + 4kl + k + 21² + 21EZ, we see ab? is odd. A. None of the above. В. If a or b is even, then ab is even. If ab' is even, then a is even or b is even. D. O DIf a and b are even, then ab is even. O E: If ab? is even, then a and b are even.
Transcribed Image Text:For the following proof, determine which of the statements given below is being proved. Proof. Assume a and b are odd integers. Then a = 2k + 1 and b = 21+1 for some k,lEZ. Then ab? = (2k + 1)(2/+ 1)2 = 8k/² + 8kl + 2k + 412 + 41+ 1=2(4kl? + 4kl + k +212 +21) + 1. Since 4kl + 4kl + k + 21² + 21EZ, we see ab? is odd. A. None of the above. В. If a or b is even, then ab is even. If ab' is even, then a is even or b is even. D. O DIf a and b are even, then ab is even. O E: If ab? is even, then a and b are even.
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