Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all (x, y) ∈ A × B, (x, y) ∈ R if and only if x ∗ y > 7. Find out following: a. R in the enumeration form b. Domain of R c. Co-domain of R

Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all (x, y) ∈ A × B, (x, y) ∈ R if and only if x ∗ y > 7. Find out following: a. R in the enumeration form b. Domain of R c. Co-domain of R

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 28E

See similar textbooks

Related questions

Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (x, y)R(z, w)…

A: We will find out the required values.

Q: Let A = {x, y} and let S be the set of all strings over A. Define a relation C from S to S as…

Q: Let S ⊆ N, and for any c, d ∈ N, consider a relation R such that cRd if and only if there exists a ∈…

Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: Consider the relation R on Z defined by the rule that (a, b) E R if and only if a + 26 is even.…

Q: A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x;…

Q: A = Z*; a R b if and only if |a – b| < 2.

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

A: Topic = function

Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

Q: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

Q: 1. Given an arbitrary relation R, suppose we compute two new celations: - R1, the reflexive closure…

A: The solution is given below

Q: a Define a relation R on N by (a,b) e Rif and only if EN Which of the following properties does R…

Q: (b) Let - be the relation on C defined by z ~ w if and only if z + w e R. Proye that is an…

A: This can be solved as follows:

Q: For each n E N, we write S" := {(x1, x2, ..., In+1) E R"+1 : E? = 1}. (1) Let f : S2 → Rª be the…

A: Given: Sn:=x1,x2,...,xn+1∈ℝn+1:∑i=1n+1xi2=1 for each n∈ℕ f:S2→ℝ4 is the function defined by…

Q: Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

Q: A relation R on a set S is said to be transitive ifffor all x, y, z ∈R, xRy ∧ yRz ⇒ xRz. Relation R…

A: It is given that A relation R on a set S is said to be transitive ifffor all x, y, z ∈R, xRy ∧ yRz ⇒…

Q: Let ≥ be a relation defined on sets A and B by A ≥ B iff there exists a surjective function f : A →…

Q: Let S be the following relation on C\{0}: S = {(x, y) = (C\{0})² : y/x is real}. Prove that S is an…

Q: Let R be a relation on the set of all functions from Z to Z defined by: R = {(f,9)|f(1) = g(3) or…

Q: Given R = { (x,y) ϵ R | (x+y) divides 3 with zero remainder, x,y ϵ A } on A = {1, 2, 3, 4, 5}, which…

Q: Show that the relation R on Z defined by aRb if and only if 5a−3b is even, for a, b ∈ Z, is an…

A: Let R be a relation from a set A to itself. R is said to be an equivalence relation if 1) R is…

Q: Verify that the relation "... is tangent to... at a" is an equivalence relation on the functions…

A: An equivalence relation on a set S is a relation ~ on S such that: 1) x~x for all x∈S then the…

Q: Let the relation R on the set Z be given by the condition: (x, y) E Rif and only if x4 = y4. Answer…

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: 1. Given an arbitrary relation R, suppose we compute two new relations: R1, the reflexive closure of…

A: Reflexsive closure :(a,a),R for each aA whereas transitive closure (a,c)R,for each (a,b)R (b,c),R…

Q: Define a relation R on Z as follows: For all integers m and n, mRn → 3|(m – n). Then 3R5 Α. True B.…

A: Solution:-

Q: . Define a relation on R²\{(0,0)} by letting (x₁, y₁)~(x₂,Y₂) if there exists a nonzero real number…

Q: Let S be the following relation on R: S = {(x, y) = R² :y-x is rational}. Prove that S is an…

Q: Let R be a relation from X to Y and S be its reverse relation from Y to X. Prove or disprove that R…

A: According to the given information it is required to prove/disprove that R is injective and well…

Q: Consider the relation on Z × Z given by aRb if a < b. Is R transitive. Answer yes or no…

Q: Let T be the relation in the set of real numbers IR defined by xTy of both xe [n, n+1] and ye[nin+1]…

Q: A relation * is defined on the set R-{0} by x * y if and only if xy > 0. For each of the following…

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: Which of the following definitions for the relation R (defined below) on A would constitute an…

Q: Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A…

A: Given, A=1,2,3 We can write the above set as, 1,2,3×1,2,3=1,1,,1,2,1,3,2,1,2,2,2,3,3,1,3,2,3,3

Q: a. Define a relation R on Z as follows: For all integers m and n, mRn + 3|(m – n). Then 3R5 (A) True…

Q: Let R be the relation on R defined by xRy if there exists some n∈Zsuch that y=x⋅cny=x⋅cn. Let c = 6…

A: This question contains 4 subparts. But according to Bartleby, only first three subparts can be…

Q: Let R be a relation defined on Z by xRy if and only if x-y=7k for kez. The equivalence class of [5]…

A: Given relation is xRy iff x-y=7k So, equivalence class of 5 will contain ....-9, -2, 5, 12, 19,....…

Q: Let a relation R on R2 be given by (x,y)R(x’,y’) provided that x-x’ and y-y’ are integers. Prove…

Q: b) Let S = { (x, y) | x, y E R} and relation R on S defined by (x,y) R (p,q) if and only if x-p =…

Q: On P2, define a relation p(x) ~ q(x) if p(0) = q(0). (a) Show that this is an equivalence relation…

Q: Let S be the following relation on C: S = {(x, y) = C²:y-x is real}. Prove that S is an equivalence…

Q: Define a relation on Z by setting xRy if xy is even. a. Give a counterexample to show that R is not…

Q: Let R be the relation on N defined by a R b if either a | 2b or b | 2a. Is R an equivalence…

A: image is attached

Q: Let R be a relation and S its reverse. Show that R is injective if and only if S is well defined,…

A: Consider the provided question, Given that, R be a relation and S its reverse. Let R is a relation…

Q: 6. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A →B as follows: For all…

A: Answer for sub question a: Given A=9,11,12,14, B=1,2,3,4. The relation R:A→B is defined as follows:…

Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (r, y) and (z, w) in A, (x, y)R(z,w) +…

Question

Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows:
For all (x, y) ∈ A × B, (x, y) ∈ R if and only if x ∗ y > 7. Find out following:

a. R in the enumeration form
b. Domain of R
c. Co-domain of R

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 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

For any relation on the nonempty set, the inverse of is the relation defined by if and only if . Prove the following statements. is symmetric if and only if . is antisymmetric if and only if is a subset of . is asymmetric if and only if .
2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric or transitive. Justify your answers. a. if and only if . b. if and only if . c. if and only if for some in . d. if and only if . e. if and only if . f. if and only if . g. if and only if . h. if and only if . i. if and only if . j. if and only if . k. if and only if .
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.