. A) Write the ordered pairs, graphical representation, and the relation matrix, for  the Relation R ‘is a factor of’, on set A{1,2,3,6}. B) determine if the relation R is reflexive, irreflexive, symmetric, antisymmetric, or transitive

Q: Let A C B and let S be an equivalence relation on B. Prove that R = {(x,y) E A × A : (x, y) E S} %3D…

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Q: Consider the matrix representing a relation R on the set {x, y, z}. 0 1 0 1 0 1 1 0 1 List…

A: To list the pairs in the relation.

Q: Let A = {x, y, z}. Write down a relation R on A that is not reflexive, not sym- metric, and not…

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Q: 11. ( a) b) c) ) Consider the relation on A={1,2,3) represented by the matrix Determine if the…

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Q: Let R be the relation defined on P({1,., 100}) by ARB if and only if |AU B| is even. Is R reflexive?…

A: Given:  R is a relation defined on P 1, 2, … , 100 by A R B  if and only if A ∪ B is even. We have…

Q: Exercise 1. Let R = {(x, y) | x, y E Z and x + y = 0, } be a relation on Z. Prove or disprove if R…

A: Let S be a non-empty set and R be a binary relation on S. (a) The relation R is said to be reflexive…

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: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

A: Relation as a Matrix: Let A = {a1,a2,a3,.......am} and B = {b1,b2,b3......bn} are two finite sets,…

Q: Let A= {1, 2, 3, 4} and let the relation R on A be defined by the matrix [1110 0101 MR then which of…

A: Given that A=1,2,3,4. The adjacency matrix of the vertices in A is given by the relation R as…

Q: b) Check whether the relation R on the set S = {1, 2, 3} with the the matrix 1 1 1 0 1 1 1 1 1 is an…

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Q: B and let R = {(x, y) E A x A | g(x) = g(v)}. Suppose g: A Show that R is an equivalence relation on…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

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

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Q: 1- R1 = {(A, B) E P(X) × P(X)/A S B} 2- R2 = {(A, B) E P(X) × P(X)/AN B + 0} %3D

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Q: a) A computer program consists of five modules M1, M2, M3, M4, and M5. A relation R on the set of…

A: From the relation matrix for R we observe that…

Q: A. Let R be a relation on set A. A={x : x ∊ J and 0 ≤ x ≤ 12},  and R={(a,b) :  a - b  is multiple…

A: Since not particular question asked ,as per guidelines solution to only first question (i.e A) is…

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…

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Q: Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the…

A: Given a relation R on the set B as "is factor of" B=1,2,3,6. a The ordered pair is…

Q: Question 5: Check whether the relation R in R defined as R = {[a, b): as b} is reflexive, symmetric…

A: Introduction :--

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

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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: Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?,…

A: Disclaimer: Since you have  asked multiple question ,we will solve first question for you . if you…

Q: A. Let R be a relation on set A. A={x : x E J and 0sxs 12}, and R={(a,b) : la - b| is multiple of 4}…

A: There are two questions given and it is discrete math. The solution to the above questions is given…

Q: 5. Let R be a relation on R2 defined by (w1,y1)R(x2y2) if and only if yı +x1 = y2 + x2. (a) Is R…

A: Given relation is

Q: Suppose that each of R ad T is a relation on a set A, the matrix for R is MB, and he matrix for T is…

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Q: (b) Let B = {r, t, s} and R2 is a relation on set defined by the following matrix [1 1 1] 0 1 0 0 0…

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Q: A relation R is defined on Z by a R b if |a – b| < 2. Which of the properties reflexive, symmetric…

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Q: 4.4.4 List the relation on N defined bv h(x, y) e N x N : x > y } 9 Scanned with CS CamScanner as a…

A: The relation given is already a subset of the Cartesian product N x N. It can be written as follows.

Q: The matrix representation for the relation R on {v1, v2, v3, v4} is given below. The first…

A: We will use the concept of adjacency matrix to write the ordered pairs of the given matrix

Q: Suppose that the matrix representation of a relation is given by 1 1 11 0 1 1 1 0 0 1 1 0 0 0 1 MR…

A: Given that the matrix representation of a relation is MR=1111011100110001

Q: Let A = {1,2, 3,4} and R a relation on A whose matrix is MR = [1 0 1 1 %3D 0 10 1 0 0 1 0 10 1 1 1…

A: Given-  A=1,2,3,4 Relation R on A whose matrix is MR=1011010100101011

Q: [1 1 1] Consider the following zero-one matrix 0 1 1 representing a relation on the ordered set {a,…

A:

Q: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: Given X = {1,3,5}. R is a relation on X, defined by aR,b if and only if la – bl is an even integer.…

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Q: 11. ( a) b) c) [1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 0 1 1…

A: 11. Consider the relation on A = {1, 2, 3} represented by the matrix 111010011   (a) To determine:…

Q: Let R be a relation on the set A = {a, b, c, d} described by the matrix MR=(1 0 0 1          0 1 0…

A: We will use the given matrix to write R in the ordered pair form and then we will find domain and…

Q: Let R be the relation defined on P({1,., 100}) by ARB if and only if |AU B| is even. s R reflexive?…

A: We will check one by one what properties R satisfies and which not.

Q: Let P=[[a.b,d).[c.f).le.g]] be a partition. Write the relation matrix for the implied equivalence…

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Q: Given a relation matrix, write the relation R in set and determine whether it is reflexive,…

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Q: Let A = {1,2, 3,4} and R a relation on A whose matrix 1 1 1 1 1 1 is Mr = 1 1 1 1 1 Determine…

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Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…

A: Explanation of the answer is as follows

Q: 11./ a) b) c) 1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine…

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Q: 2. Given a relation, R on A = {a, b, c, d} on as follows: %3D R = {(a, a), (a, b), (a, d), (b, b),…

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Q: Let R be the relation defined on P({1,.…, 100}) by ... ARB if and only if |AUB| is even. Is R…

A: Relation: - A subset of the productA× B could be a relation R from a non-empty set A to a non-empty…

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,…

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Q: 11. ( a) b) c) ) Consider the relation on 4= {1,2,3) represented by the matrix 0 Determine if the…

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Q: A. Let R be a relation on set A. A={x : x ∊ J and 0 ≤ x ≤ 12}, and R={(a,b) : a - b is multiple of 4…

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Q: . Let R be the relation on Z→ Z such that ((a,b),(c,d)) eR = a+d =b+c. Show that R is an equivalence…

A: An equivalency relation on a set is a reflexive, symmetric, and transitive relationship for…

Q: 3. Use the cross product properties to prove the relation (a - b) × (â+b) = 2(â × b) given a = (1,…

A: Given,a=i-3j+2kb=-2i+0j+k

Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

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Q: b) Let C = {1, 2, 3, 4}. Find a relation R on C that has exactly 3 ordered pair members and is both…

A: Given C = {1, 2, 3, 4}. We find a relation R on C that has exactly 3 ordered pair members and  both…