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

See similar textbooks

Similar questions

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.
. Let R1, R2, R3 be relations on { a, b, c, d, e }. Find the transitive closures, given their definitions below. i) R1 = { (a, c),(b, d),(c, a),(d, b),(e, d) } ii) R2 = { (b, c),(b, e),(c, e),(d, a),(e, b),(e, c) } iii) R3 = { (a, b),(a, c),(a, e),(b, a),(b, c),(c, a), (c, b),(d, a),(e, d) }
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)}
How do you solve this question on discrete mathematics: 2. Let A be the set of all points in three-dimensional space. Define R as the relation that two points will have the same z coordinate. (a) Give three examples that are related to P(4,6,2). (b) Prove or disprove that R is reflexive. (c) Prove or disprove that R is symmetric. (d) Prove or disprove that R is transitive. (e) Is R an equivalence relation? (f) What space do all points related to each other (e.g. all points withz= 2) describe?
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)
The binary relation {(1,1), (2,1), (2,2), (2,3), (3,1), (3,2)} on the set {1, 2, 3} is O reflexive, symmetric, and transitive transitive O antisymmetric O anstisymmetric and transitive

Recommended textbooks for you

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elementary Geometry for College Students

Geometry

ISBN:

9781285195698

Author:

Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:

Cengage Learning

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elementary Geometry for College Students

Geometry

ISBN:

9781285195698

Author:

Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

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