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(2) Let R = { (a, b) E Z² : 3a – 36 = 4q for some integer q (a) Prove the relation is transitive. (b) Prove the relation is not antisymmetric. TI Here are some definitions that may be useful: A binary relation R on set A is reflexive: for each a E A, (a, a) E R. A binary relation R on set A is symmetric: for each a, b e A, if (a, b) E R then (b, a) E R. A binary relation R on set A is antisymmetric: for each a, b e A, if (a, b) E R and (b, a) E R then a = b. A binary relation R on set A is transitive: for each a, b, c E A, if (a, b) E R and (b, c) E R then (a, c) e R.

(2) Let R = { (a, b) E Z² : 3a – 36 = 4q for some integer q (a) Prove the relation is transitive. (b) Prove the relation is not antisymmetric. TI Here are some definitions that may be useful: A binary relation R on set A is reflexive: for each a E A, (a, a) E R. A binary relation R on set A is symmetric: for each a, b e A, if (a, b) E R then (b, a) E R. A binary relation R on set A is antisymmetric: for each a, b e A, if (a, b) E R and (b, a) E R then a = b. A binary relation R on set A is transitive: for each a, b, c E A, if (a, b) E R and (b, c) E R then (a, c) e R.

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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(2) Let R = { (a, b) e Z² : 3a – 3b = 4q for some integer q}. (a) Prove the relation is transitive. (b) Prove the relation is not antisymmetric. NTIAL Here are some definitions that may be useful: A binary relation R on set A is reflexive: for each a E A, (a, a) E R. A binary relation R on set A is symmetric: for each a, b e A, if (a, b) E R then (b, a) E R. A binary relation R on set A is antisymmetric: for each a, b e A, if (a, b) E R and (b, a) E R then a = b. A binary relation R on set A is transitive: for each a, b, c E A, if (a, b) E R and (b, c) E R then (a, c) E R.
Transcribed Image Text:(2) Let R = { (a, b) e Z² : 3a – 3b = 4q for some integer q}. (a) Prove the relation is transitive. (b) Prove the relation is not antisymmetric. NTIAL Here are some definitions that may be useful: A binary relation R on set A is reflexive: for each a E A, (a, a) E R. A binary relation R on set A is symmetric: for each a, b e A, if (a, b) E R then (b, a) E R. A binary relation R on set A is antisymmetric: for each a, b e A, if (a, b) E R and (b, a) E R then a = b. A binary relation R on set A is transitive: for each a, b, c E A, if (a, b) E R and (b, c) E R then (a, c) E R.
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