*********** Use the definitions of even, odd, prime, and compositive numbers to justify your answers for (a)-(c). Assume that r and s are particular integers. (a) Is Srs even? O Yes, because 8rs = 2(4rs) + 1 and 4rs is an integer. O Yes, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) + 1 and 4rs is an integer. (b) Is 2r + 4s² + 9 odd? O Yes, because 2r + 4s² + 9 = 2(r + 2s2 + 4) + 1 and r + 2s² + 4 is an integer. O Yes, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) + 1 and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. (c) If r and s are both positive, is 2² + 2rs + s² composite? O Yes, because ² + 2rs + s² = (r + s)2 and r + s is an integer. O Yes, because r2 + 2rs + s2 = (r + s)2 and r + s is not an integer. O No, because 2² + 2rs + s² = (r + s)2 and r + s is not an integer. O No, because 2 + 2rs + s² = (r + s)2 and r + s is an integer.
*********** Use the definitions of even, odd, prime, and compositive numbers to justify your answers for (a)-(c). Assume that r and s are particular integers. (a) Is Srs even? O Yes, because 8rs = 2(4rs) + 1 and 4rs is an integer. O Yes, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) + 1 and 4rs is an integer. (b) Is 2r + 4s² + 9 odd? O Yes, because 2r + 4s² + 9 = 2(r + 2s2 + 4) + 1 and r + 2s² + 4 is an integer. O Yes, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) + 1 and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. (c) If r and s are both positive, is 2² + 2rs + s² composite? O Yes, because ² + 2rs + s² = (r + s)2 and r + s is an integer. O Yes, because r2 + 2rs + s2 = (r + s)2 and r + s is not an integer. O No, because 2² + 2rs + s² = (r + s)2 and r + s is not an integer. O No, because 2 + 2rs + s² = (r + s)2 and r + s is an integer.
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:Use the definitions of even, odd, prime, and compositive numbers to justify your answers for (a)-(c). Assume that r and s are particular integers.
(a) Is Srs even?
O Yes, because 8rs = 2(4rs) + 1 and 4rs is an integer.
O Yes, because 8rs = 2(4rs) and 4rs is an integer.
O No, because 8rs =
2(4rs) and 4rs is an integer.
O No, because 8rs = 2(4rs) + 1 and 4rs is an integer.
(b) Is 2r + 4s² + 9 odd?
O Yes, because 2r + 4s² + 9 = 2(r + 2s² + 4) + 1 and r + 2s² + 4 is an integer.
O Yes, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer.
O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) + 1 and r + 2s² + 4 is an integer.
O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer.
(c) If rand s are both positive, is r² + 2rs + s² composite?
O Yes, because 2² + 2rs + s² = (r + s)² and r + s is an integer.
O Yes, because r² + 2rs + s² = (r + s)2 and r + s is not an integer.
O No, because 2² + 2rs + s² = (r + s)² and r + s is not an integer.
O No, because 2 + 2rs + s² = (r + s)2 and r + s is an integer.
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