Which of the following sets are subrings of the field R of real numbers? (a) A = {m+n√√2 | m, n = Z and n is even} (b) B = {m+n√√2 | m, n = Z and m is odd} (c) C = {a+b√√2 | a, b = Q} (d) D = {a+b√√/3 + c39 | a, b, c = Q} C (e) E = {m+nu | m, n = Z}, where u = (1+√√3)/2 (f) F = {m + nv | m, n = Z}, where v = (1 + √5)/2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Which of the following sets are subrings of the field R of real numbers?
(a) A = {m+n√√2
m, n e Z and n is even}
(b) B = {m+n√√2 | m, n € Z and m is odd}
(c) C = {a+b√2 | a, b = Q}
(d) D = {a+b√√3+c9|a, b, c = Q}
(e) E = {m + nu | m, n = Z}, where u = (1+√√3)/2
(f) F = {m + nv | m, n = Z}, where v = (1 + √5)/2
Transcribed Image Text:Which of the following sets are subrings of the field R of real numbers? (a) A = {m+n√√2 m, n e Z and n is even} (b) B = {m+n√√2 | m, n € Z and m is odd} (c) C = {a+b√2 | a, b = Q} (d) D = {a+b√√3+c9|a, b, c = Q} (e) E = {m + nu | m, n = Z}, where u = (1+√√3)/2 (f) F = {m + nv | m, n = Z}, where v = (1 + √5)/2
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