1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b if a - b is rational. (b) S = C, the complex numbers, ab if |a| = |b|. (c) S = straight lines in the plane, a ~ b if a, b are parallel. (d) s = set of all people, a ~ b if they have the same color eyes.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Verify that the relation is an equivalence relation on the set S given.
(a) S = R reals, ab if a - b is rational.
(b) S = C, the complex numbers, ab if |a| = |b|.
(c) S = straight lines in the plane, a ~ b if a, b are parallel.
(d) S = set of all people, a ~ b if they have the same color eyes.
Transcribed Image Text:1. Verify that the relation is an equivalence relation on the set S given. (a) S = R reals, ab if a - b is rational. (b) S = C, the complex numbers, ab if |a| = |b|. (c) S = straight lines in the plane, a ~ b if a, b are parallel. (d) S = set of all people, a ~ b if they have the same color eyes.
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