Let set A = {1,2,3,4} and let R1 and R2 be binary relations on A. Specifically, let: R1 = {(1,1), (1,2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4, 3) (4, 4)} R2 = {(1,2), (1,3), (1, 4), (2, 1), (2,3), (4, 1), (4, 2)} Determine the following: a) Whether R, is reflexive, irreflexive, symmetric, anti-symmetric and/or transitive. b) Whether R, is reflexive, irreflexive, symmetric, anti-symmetric and/or transitive. c) R1 • R2.

Let set A = {1,2,3,4} and let R1 and R2 be binary relations on A. Specifically, let: R1 = {(1,1), (1,2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4, 3) (4, 4)} R2 = {(1,2), (1,3), (1, 4), (2, 1), (2,3), (4, 1), (4, 2)} Determine the following: a) Whether R, is reflexive, irreflexive, symmetric, anti-symmetric and/or transitive. b) Whether R, is reflexive, irreflexive, symmetric, anti-symmetric and/or transitive. c) R1 • R2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Explain why each of the following binary relations on S = {1, 2, 3} is not an equivalence relation…

Q: 9. Represent the following relations on A = {1, 2, 3, 4, 5, 6} using a matrix and a digraph. (a) R =…

A: Given that , A = { 1,2,3,4,5,6}

Q: Identify the matrix that corresponds to the relation {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)).…

Q: Let A= {1,2,x,y,z}, and B= {1,2,3,z}. How many distinct elements are in (A*B) intersect (B*A

A: Given that A=1,2,x,y,zB=1,2,3,z To find the number of distinct elements in A×B∩B×A:

Q: Let R be a relation on the set A = {0, 1, 4, 8} defined by xRy if and only if x + y < 8. (i) List…

Q: R, S, and T are relations defined on A {0, 1, 2, 3}. Let S = {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

Q: MR₁ = To Let R₁ and R₂ be relation on a set A represented by the matrices 50 1 07 1 1 0 1] 0 1 0 1 1…

A: The objective of the question is to find the matrices that represent the union, intersection, and…

Q: 10 1 Let R be the relation represented by the matrix MR and S be the relation represented by the…

Q: Let R1 = {(1,1), (2,2)} and R2 = {(1,1), (1, 2)} be relations on A = {1,2}. Then R1 UR

A: In this question given that two sets R1 and R2 and we find the unions of these sets and relation of…

Q: and -5 Compute ū - v. 2

A: Given Formula :

Q: Suppose that A = {1, 2, 3} and B = {4, 6}. Let R be the relation from A to B containing (a, b) if a…

Q: B2. (a) [2 Marks ] Show that the relation R in the set {1,2,3} given by R = {…

Q: Let A = {1, 2, 3, 4, 5, 6}, and consider the following equivalence relation on A: R = {(1, 1), (2,…

Q: Let G={1,-1,i,-i} with usual multiplication then G is isomorphic to Select one: a. Z, x Z, b. (Z, +)…

Q: Let A={ 1, 2, 3, 4, 5} R={ (1,1), (1,2), (2,1), (2,2), (3,3), (3,4), (4,3), (4,4), (5,5) } Write the…

Q: Let R = {(3,4),(1,3),(4,2),(4,1)}, Then R² is given by O (1,3),(2,1),(3,2),(4,3)} O {(1,3).(2,1).(3,…

Q: What is the kernel and image of the map

Q: Draw the arrow diagram for each composition of relations S and T represented by matrices: S: 101 T:…

A: The two relations S and T represented in matrix form are S= 101 011…

Q: 010 = Let R₁ and R₂ be relations on a set A represented by the matrices MR₁ 1 1 1 and MR₂ = 100 ГА В…

A: Given that R1 and R2 be the relations on set A represented by the matrices…

Q: Let R₁ and R₂ be relation on a set A represented by the matrices [0 1 0] 1 1 0 го о 17 MR₁ = 0 1 0…

A: and We have to find the matrix representation and .

Q: Q-3: a) Let R be a relation on A = {1,2,3,4} such that aRb means |ab| ≤ 1. Find the matrix…

A: (a) It is given that, R be a relation on A = {1, 2, 3, 4} such that aRb ⇔ a-b≤1 We have to find the…

Q: a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an…

Q: a3 and b Let a₁ a2 Determine whether b can be written as a linear combination of a₁, 32, and a3. In…

Q: There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (1) {(0,…

Q: Suppose f : B C where B = {a, b, c}, C = {2, 8, 10}, and f is defined by f = {(a, 8), (b, 10), (c,…

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

Q: 1. Given A = {1, 2, 3, 4}, B = {a, ß,7} and R= {(2,B), (2, 7), (4, B), (1, a), (1, 7)} (a) Determine…

A: Here given that A={1, 2, 3, 4} B={α, β, γ} And…

Q: Let S = {0, 1, 2, 4, 6}. Test the following relation whether it has equivalence relation on S. R =…

A: Given relation R = {(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (0, 1), (0, 2), (1, 2), (4, 6)} on S =…

Q: Which relations are partial order? O None of the propsed relations O A={5,6,8,10,20} and R={ (a,b) e…

Q: If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, what is the reflexive closure of R? O {(1, 2), (2,…

A: The Second option is correct {(1,1),(1,2),(1,4),(2,2),(2,3),(3,1),(3,3),(4,2),(4,4)}

Question

Let set A = {1,2,3,4} and let R1 and R2 be binary relations on A. Specifically, let:
R1 = {(1,1), (1,2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4, 3) (4, 4)}
R2 = {(1,2), (1, 3), (1, 4), (2, 1), (2,3), (4, 1), (4, 2)}
Determine the following:
a) Whether R, is reflexive, irreflexive, symmetric, anti-symmetric and/or transitive.
b) Whether R, is reflexive, irreflexive, symmetric, anti-symmetric and/or transitive.
c) R1 • R2.
d) R2 • R1.
e) R1 U R2.
f) Rz n R2.
g) The reflexive, symmetric, and transitive closures of both R, and R2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Please just answer parts iv. and v.
Let R be an equivalence relation on A = {0, 7, 8, 9} and R = {(7, 8), (8,9), (9, 9), (7, 7), (8, 8), (7, 9), (9, 7), (9, 8), (8, 7), (0, 0)}. Answer each of the following questions. [8] = [7] = [9] = [0] =
Let U={1,2,3,4,5,6,7,8,9,10} Let A={1,2,3,8,9}. LetB={1,4,5,6,8}. Determine (A−B)′
Prove or disprove reflexivity, symmetry and transitivity of R.
Let A = {0,1,2,3} and R a relation over A: R = {(0,0),(0,1),(0,3),(1,1),(1,0),(2,3),(3,3)} Check whether R is an equivalence relation or a partial order. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation or a partial order.
Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive
Choose the answer
9
Which of the following relations is the a partial ordering on the set A = {3,7,9}? {(3,3),(7,7), (3,9),(9,7), (9,9)} O {(3,3),(7,7),(7,9),(9,9), (9,7)} O 3,3,7,7,9,9,3,7,7,9,3,9 O None of the others O {(3,3),(3,7),(7,9),(7,7),(9,9)}
Explain whny the following binary relation on. 1,2,3} Is not R= {(1,1)(1,2),(1,3),(2,1).(2,2).(3,3)}|
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