5.• S contains (w, x) and (2, u).• Sis not antisymmetric.• is not symmetric.• is not transitive.|S| 2 4.|S| < 6.S satisfies all of the following requirements:Construct a binary relation S defined on the set {u, v, w, r, y, z} such thatCC HKU SPACHKU SPACE CSPACE CCCEKU

The binary relation based on given set {u,v,w,x,y,z}

Answered: 5. • S contains (w, r) and (2, u). • S…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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a ) Let R be the relation on the set A={1,2,3,4} defined by aRb if and only if 2a>b+1. Find the matrix representing R∘R. b) Suppose that the relation R is defined on the set Z where aRb means a= ±b. Show that R is an equivalence relation.i would like to get a non handwriting answer to be easy to cope please
(b) Let R = {(1, 1),(1, 2),(2, 1),(2, 2), (3, 3)}. be a relation on a set A= 1,2,3} , the R is %D Antisymmetric and transitive. ii. i. Not antisymmetric, and not transitive Antisymmetric, and not transitive Non of these iii. iv.
3. For universe S = R2 define relation ~ as: (a, b) ~ (c,d) — 2a-b2c - d. Prove that is an equivalence relation on R2, or find a counterexample.
6. Give an example of a relation Ron A = {-1, -3, -5} such that: (a) Ris both symmetric and antisymmetric. (b) Ris neither symmetric nor anris ymmetric. (c) Ris transitive, but RUR- is not transitive.
2. Let A := {1,2,3,4}: B and T:= {(a, b) E A x B | +¹ € Z}. (a) Find A x B. (b) Find T. (c) Check what property of Relations thus T have. Provide a brief explana- tion for each property.
2. For each of these relations on the set {1, 2, 3, 4), decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)} c) {(2, 4), (4, 2)} d) {(1, 2), (2, 3), (3, 4)} e) {(1, 1), (2, 2), (3, 3), (4,4)} f) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)}
(b) Let R = {(1, 1), (1, 2),(2, 1), (2, 2),(3, 3)}. be a relation on a set A = {1,2,3} , the R is Antisymmetric and transitive. ii. i. Not antisymmetric, and not transitive Antisymmetric, and not transitive iv. iii. Non of these
2. Let R be the relation on Z→Z such that ((a,b),(c,d))eR a+d =b+c. Show that R is an equivalence relation.
b) Let C= {1, 2, 3, 4}. Find a relation R on C that has exactly 3 ordered pair members and is both irreflexive and antisymmetric. (2 marks)

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5. • S contains (w, r) and (2, u). • S is not antisymmetric. • S is not symmetric. • is not transitive. |S| 2 4. IS| < 6. S satisfies all of the following requirements: Construct a binary relation S defined on the set {u, v, w, r, y, z} such that CC HKU SPA KU SPACE CO SPACE CC CE ku HKU