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Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean geometry, there exists exactly one line parallel to a given line. II. In Lobachevskian geometry, there are no parallel geodesics. III. In Riemannian geometry, at least 2 lines are parallel to a given line. O Statements I and III only None of the statements Statements II and III only O Statement II only O Statement Ill only Statements I, II, and III Statements I and II only O Statement I only

Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean geometry, there exists exactly one line parallel to a given line. II. In Lobachevskian geometry, there are no parallel geodesics. III. In Riemannian geometry, at least 2 lines are parallel to a given line. O Statements I and III only None of the statements Statements II and III only O Statement II only O Statement Ill only Statements I, II, and III Statements I and II only O Statement I only

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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Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean geometry, there exists exactly one line parallel to a given line. II. In Lobachevskian geometry, there are no parallel geodesics. III. In Riemannian geometry, at least 2 lines are parallel to a given line. O Statements I and III only None of the statements Statements II and III only O Statement II only O Statement Ill only Statements I, II, and III O Statement I only O Statements I and II only
Transcribed Image Text:Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean geometry, there exists exactly one line parallel to a given line. II. In Lobachevskian geometry, there are no parallel geodesics. III. In Riemannian geometry, at least 2 lines are parallel to a given line. O Statements I and III only None of the statements Statements II and III only O Statement II only O Statement Ill only Statements I, II, and III O Statement I only O Statements I and II only
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