Let A = {1,2} and B = {1,2}. Which of the following gives a relation satisfying the condition that (x,y) is an element of R where x – y is a natural number. a. {(1,1),(1,2),(2,1),(2,2)} b. {(1,1), (2,2)} c. {(2,1),(2,2)} d. {(2,1)}

Let A = {1,2} and B = {1,2}. Which of the following gives a relation satisfying the condition that (x,y) is an element of R where x – y is a natural number. a. {(1,1),(1,2),(2,1),(2,2)} b. {(1,1), (2,2)} c. {(2,1),(2,2)} d. {(2,1)}

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 1E: For determine which of the following relations onare mappings from to, and justify your answer. ...

See similar textbooks

Related questions

Q: List the ordered pairs in the relation R from A ={0,1,2,3} to B = {0,1,2,3} where (a,b) ϵ R, if and…

Q: Let A={3,4,6,7}, and define a relation R on A as follows: For every x, y belong to A, xR y x|y.…

A: We first write elements of R then we form diagraph and then we write the corresponding adjacency…

Q: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: 0,1,2

Q: Show that the relation R on a set A is symmetric if and only if R = R-, where R is the inverse…

Q: 1. Let R be a relation on R x R such that (*1vi)Rs02) if and only if x,yı = x2y2. (a) Is (2,3)R(1,4)…

A: A relation from a set A to B is defined as a subset of A×B. Here R is a relation on ℝ×ℝ such that…

Q: ist the ordered pairs in the relation R from A = 0, 1,2, 3, 4, B = 1,2, 3, 4, 5, where Ris defined…

Q: Ppply the necessory for the given restrictions relation Ques tion 1 in order for it o be bi gec tive…

Q: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

Q: 1 In the relation . If R, =1 and %3D R R R, R,%3D3, find R.

Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y^x, y = A} R"X =…

Q: Define the following relations on A = {0, 1,2, 4}. Answer each of the following questions by listing…

A: We will use the basic definitions

Q: Let A={1,2,3} and B={-2,-1,0}. Define a relation R from S to T as follows: For all (x,y) in AxB,…

Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

Q: Let A = {3,4,5,6} and B = {1,2,3} and define a relation R: A → B as follows: For all (x, y) ∈ A × B,…

Q: C. Let T be defined onN N by (a, b)T (c, d) if and only if a c and b 2 d. Write down the full nature…

A: We will use the basic definition of reflexive, symmetric, antisymmetric and transitive realtion.

Q: Suppose z = z(x,y) is x + y+z = e¬(x+y+z) , then which relation is correct? az D): az az az az 1 ду…

A: The solution is given as follows :

Q: on B on the set A = {1, 2, 3, 4}: It is defined as, xBy ⟺ x|y

A: The relation β on set A={1,2,3,4} is defined as xβy↔x/y this means that β has elements such that…

Q: Let A = {0,1,2} and B = {-2,-1,0}. Define a relation C from A to B as follows: For any (x,y) A x B,…

Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

Q: Which of the following is/are true for the relation R, where a is related to b (aRb), if and only if…

A: Suppose, A be any set and suppose R:A->A is a relation. Then, R is reflexive: if for every x in…

Q: Let G = {-2,0, 2} and H = {4,6,8} and define a relation V from G to H as follows: %3D For all (x, y)…

A: Solve the following

Q: 9. Let X = {r1,12, 23, T4}, Y = {yı,y2, Y3}, and Z = {zı, z2}, Let R be the relation from X to Z…

A: Given: 9) X=x1, x2, x3, x4, Y=y1, y2, y3 and Z=z1, z2, z3. R=x1, z1, x2, z2, x3, z1, x3, z2 and…

Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

Q: Let R be the relation on the set S = {1,2, 3, a, b, c} given by xRy if and only if (x, y) E {(a, a),…

A: S=1,2,3,a,b,c To find: (a) , (b) , (c).

Q: Define a relation C from R to R as follows: For any (x, y) £ R x R. (x, y) C means that x² + y²…

A: Given: Define a relation C from R to R as follows,for any (x,y)∈R×R (x,y) C means that x2+y2=4

Q: Let : [0, 1] → [0.c], te- and let w be a 1-form on R. What and foe, and why? is the relation between…

Q: - List the ordered pairs in the relation R from A = (0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,b)…

Q: 5. Let A = {1, 2} and B x+y y) e R such that {3,4}and define a relation from A to B as (x,y) e AxB…

A: We will find out the required values.

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

Q: List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B {0, 1, 2, 3}, where (a,b) e R…

Q: Let S = {1,2,3,... 18} and define the relation R by xRy if xly. Draw the Hasse diagram for R.

Q: Define a relation C from R to R as follows: For any (x,y) R x R, (x,y)C meaning that x2 + y2 = 1…

A: Given

Q: Given R = { (x,y) ϵ R | x = (y+1), x,y ϵ A } on A = {1, 2, 3, 4, 5}, which of the following…

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

Q: . Draw the Hasse diagram of the relation R on A, where A = (1, 2, 3, 4}, and R = {(1, 1), (1, 2),…

Q: Let E =(1, 2, 3} and F = {-2, -1, 0} and define a relation T from E to F as follows: For all (x, y)…

Q: Let A = {4, 5, 6} and B = {5, 6, 7} and define relations R, S, and T from A to B as follows: %3D For…

A: Relation R is defined as:

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

Q: Determine which of these relations are transitive. The variables x, y, x', y' represent integers.…

Q: Define a relation R on the set J ={ 0, 1, 3, 4, ,5, 6 } as follows for all x, y E J x R y if and…

Q: Let fi = 1+x + æ?, f2 = 3+ 2x + a?, fs = 1+ 2x + 3x?, fa = 1+ 3x + 5æ?. 1 -1 is a dependence…

Q: Define the following relations on A = {0, 1,2,4}. Answer each of the following questions by listing…

A: I am going to solve the given problem by using some simple algebra to get the required result of the…

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

Q: Let A = {#, 7, x} and let R be the relation on A given by R = {(7, 7), (#, #)}

A: R is said to be reflexive relation on A if for all x in A, xRx holds. R is said to be symmetric…

Q: One of the followin relations is not symmetric,where A={1,2,3,4}: .a…

Q: the 品|名 Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A b) as follows: For every (x,…

A: using the concept of relation ...

Q: In this exercise, you want to show that a relation RC A? is transitive + R"C R for all n E N = {1,2,…

Q: Given A = {1,2, 3, 4} and B = {x,y , z}. Let R be the following relation from A to B: R =…

A: Given A=1,2,3,4 and B=x,y,z Let R be the following relation from A to B such that…

Question

Let A = {1,2} and B = {1,2}. Which of the following gives a relation satisfying the condition that (x,y) is an element of R where x – y is a natural number.

a. {(1,1),(1,2),(2,1),(2,2)}

b. {(1,1), (2,2)}

c. {(2,1),(2,2)}

d. {(2,1)}

Expert Solution