(b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive? 14. Let and be relations on R defined as follows: • For x, y e R, x y if and only if xy > 0. • For x, y E R, X y if and only if xy < 0. (a) Is ~ an equivalence relation on R? If not, is this relation reflexive, symmetric, or transitive? (b) Is an equivalence relation on R? If not, is this relation reflexive, symmetric, or transitive? 15. Define the relation on R x R as follows: For (a, b) , (c, d)eRx R, (a, b) (c, d) if and only if a? +b2 = c² + d2. (a) Prove that is an equivalence relation on R x R. (b) List four different elements of the set C = {(x, y) e R x R| (x, y) (4, 3)}.
(b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive? 14. Let and be relations on R defined as follows: • For x, y e R, x y if and only if xy > 0. • For x, y E R, X y if and only if xy < 0. (a) Is ~ an equivalence relation on R? If not, is this relation reflexive, symmetric, or transitive? (b) Is an equivalence relation on R? If not, is this relation reflexive, symmetric, or transitive? 15. Define the relation on R x R as follows: For (a, b) , (c, d)eRx R, (a, b) (c, d) if and only if a? +b2 = c² + d2. (a) Prove that is an equivalence relation on R x R. (b) List four different elements of the set C = {(x, y) e R x R| (x, y) (4, 3)}.
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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I need help with 14 please
Transcribed Image Text:(b) Is an equivalence relation on Z? If not, is this relation reflexive,
symmetric, or transitive?
14. Let and be relations on R defined as follows:
• For x, y e R, x y if and only if xy > 0.
• For x, y E R, X y if and only if xy < 0.
(a) Is ~ an equivalence relation on R? If not, is this relation reflexive,
symmetric, or transitive?
(b) Is an equivalence relation on R? If not, is this relation reflexive,
symmetric, or transitive?
15. Define the relation on R x R as follows: For (a, b) , (c, d)eRx R,
(a, b) (c, d) if and only if a? +b² = c2 + d2.
(a) Prove that is an equivalence relation on R x R.
(b) List four different elements of the set
C = {(x, y) E R x R | (x, y) (4, 3)}.
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