Let a relation S be defined on A = {0, 1, 2, 3} as follows.S = {(0, 0), (0, 3), (1, 0), (1, 2), (2, 0), (3, 2)}Find St, the transitive closure of S. Let a relation S be defined on A = {0, 1, 2, 3} as follows.S = {(0, 0), (0, 3), (1, 0), (1, 2), (2, 0), (3, 2)}Find S, the transitive closure of S.S, = {(0, 2), (1, 3), (2, 2), (2, 3), (3, 0), (3, 3)}

Answered: Image /qna-images/answer/2321e43d-c321-4fac-a06e-1ac360ea6d79.jpg

Answered: Let a relation S be defined on A = {0,…

Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2, 0), (3, 2)} Find S, the transitive closure of S.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 24E: For any relation on the nonempty set, the inverse of is the relation defined by if and only if ....

See similar textbooks

Related questions

Q: Let A = (1, 2, 3, 4, 6). Let Ri be a relation defined on A. a. Verify reflexive property on the…

A: "Hi! Thank you for the question! Since the question contains four subparts and we are allowed to…

Q: 2) Let Q = {0,1,2,3} and define relation R on Q as follows: R = {(0,0), (0,1), (0,3), (1,0), (1,1),…

Q: Let A = {1, 2, 3, 4, 6}. Let Ri be a relation defined on A. a. Verify reflexive property on the…

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: Let a relation S be defined on A = {0, 1, 2, 3} as follows. s= {(0,0), (0, 3), (1, 0). (1, 2). (2,…

Q: 0,1,2

Q: The relation R on X={1,2,3,4}defined by (x,y) € R if x=y.

Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 3)}.…

Q: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

Q: 1 0 10 1 0 1 0 1 0 Let A = {1,2,3,4,5} and M, = 1 1 1 1 1 0 1 0 1 0 |1 0 1 0 1 a) Give the relation…

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 T = {0, 1, 2, 3} and the relation R is defined on T as follows: R {(0, 1), (1, 2), (2, 2)}. The…

Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 2)}.…

A: Given T = {0,1,2,3} and the relation R is defined on T as follows R= {(0,1),(1,2),(2,2) }

Q: Suppose that f : A → B is a function, viewed as a relation (set of ordered pairs). Let f* denote the…

Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 2)}.…

A: The symmetric closure, R(s) is calculated using the formula, R(s)=R∪R-1 , where, R-1=b,a: a,b∈R .…

Q: 8. Define a relation R on the set J = {0, 1,3,4,5,6} as follows: For all x, y EJ, x Ry ⇒ 4x² + y².…

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: 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…

A: A=3,4,5B=1,2,3,4R=x,y: x∈A, y∈B ∋xy>7 a. R=3,3, 3,4, 3,5, 4,2, 4,3, 4,5, 5,2, 5,3, 5,4, 5,5

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

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

Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 3)}.…

A: Given that, T=0,1,2,3 and the relation R is defined on T as follows: R=(0,1),(1,2),(2,3)

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: Let X = {6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 z e N₁ x + z = y}, where…

Q: Let R be the relation on Z defined by R = {(a,b): a, b ∈ Z, a – b is an integer}.Find the domain…

A: R = {(a,b): a, b ∈ Z, a – b is an integer}. We know that the difference of two integers is always an…

Q: Consider the relation R on R defined by (x, y) E R if and only if |æ – y| = ||x| – ly||- This…

Q: Let A = {1,2, 3, 4, 5,6} and R a relation on A whose MR is given below 0 100 0 1] 0 0 10 0 0 00 1 10…

A: Let R be a relation on a set A. The relation R can be represented using the matrix and the digraph.…

Q: 5. Given a function f: A → B. Define the relation f from P(A) to P(B) by f = {(X,Y)C P(A) × P(B) | Y…

Q: Let R be the relation on the set (0, 1, 2, 3} and R= {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3,…

Q: A relation R on a set A is called irreflexive iff (Vx E A)((x, x) ¢ R). It is called asymmetric iff…

Q: 3. Define a relation S from R to R as follows: For all (x, y) e R xR, (x, y) eS means that x2 y. a.…

A: Given x,y∈S Mean x≥y x,y∈R×R

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

A: We have S=x,yx,y∈R x,yRp,q if and only if x-p=y-q Reflexive property: A relation R is said to be…

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows: x1,y1≺x2,y2 if and only if x1<x2 or x1=x2 and y1≤y2

Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1). (1, 2), (2, 2)}:

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: Let X = {-2, 0, 2} and let P(X) be the power set of x (the set of all subsets of X). A relation U is…

A: Given: Here, we have X=-2,0,2 and PX is the power set of X. The relation U is defined on PX, such…

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

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

A: We will prove the given statement.

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: Discrete structure

Q: Let A be the set of all lines in the plane. Define a relation R on A as follows. For every l1 and…

Q: Define an equivalence relation on R² by: ¤1, Y1) ~ (x2, Y2) e if and only if (*1, Yı) and (x2, Y2)…

A: The complete solutions are given below

Q: Let T = {0, 1, 2, 3, 4} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 3)}.…

A: Solution...

Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (r, y) and (2, w) in A, (r, y)R(z, w)…

A: Given that: A=Z+xZ+. Relation is: For all (x, y) and (z, w) in A, (x, y)R(z, w)⇔x+w=z+y…

Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 2)}.…

Q: a) Let O be the set of odd numbers and O' = {1, 5, 9, 13, 17, ...} be its subset. Define the…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

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 relation S be defined on A = {0, 1, 2, 3} as follows.

S = {(0, 0), (0, 3), (1, 0), (1, 2), (2, 0), (3, 2)}

Find S_t, the transitive closure of S.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

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 .
Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.
For determine which of the following relations onare mappings from to, and justify your answer. b. d. f.
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.
Find mappings f,g and h of a set A into itself such that fg=hg and fh. Find mappings f,g and h of a set A into itself such that fg=fh and gh.
27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .