3. Given a relation R on a set A, prove that if R is transitive, then so is R-1.

Q: 1. Given a relation R on a set A, prove that if R is transitive, then so is R-

A: Transitive means aRb and bRc then aRc

Q: On the set A = {a, b, c, d, e, f, g, h} is given by the relation R = {(a; b), (a; c), (a; d), (a;…

A: The set is A=a, b, c, d, e, f, g, h and the relation is R=a; b, a; c, a; d, a; e, b; f, c; f, d; g,…

Q: Suppose that R is a reflexive and transitive relation on a set A. Define a new relation E on A by…

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Q: 2. Define the sets X = {1,2,3} and Y = {4,5,6}. Now, define the relation R from X to Y by „R, if and…

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Q: Prove that for any set relation R (we did not pick it to be "on" any particular set) R* =N{Q:RC Q^ Q…

A: Given that any set relation R.

Q: Given the relation R = {(u,t),(v,t),(w,t),(w,u),(w,v)} on a set A = {t,u,v,w}, what is/are the…

A: topic - relation

Q: 1. Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible…

A: According to question given that Set Z in which the relation R is defined by aRbIf and only if a+3b…

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: B if there exists o E Sn so that oao- = B. Prove that For a, B E Sn, let a ~ equivalence relation…

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Q: Assume R is a relation Dver set A. a) prove Ris anti-ceflective 1 Diaw graph G(LE) where the…

A: A relation R on a set X is said to be anti-reflective if no element  of X is related  to itself…

Q: Let R be a transitive relation on set A. Define Q to be {(r Prove or disprove that (RUR®)n (QU Qº)…

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Q: Suppose R and S are symmetric relations on a set A. Prove that RoS is symmetric iff RoS = So R.

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Q: Show that the relation R in the set A of all the books in a library of a college,given by R = {(x,…

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Q: Use a membership table to prove the following relation: * (An B) U (A n Bº) = A

A: We have to use membership table.

Q: Let the relation non z defined by x ny if and only if 3/(x+2y) Show that n is an equivalence…

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Q: 1. Prove that “divides" is a transitive relation. That is, prove that, for all integers a, b, c, if…

A: I the given question we have to prove that , for all integers a,b,c, if a|b and b|c, then a|c.

Q: 1. Let & be the relation of (a,b) la #b] on the set of integers. What is the reflexive closure of R?

A: As per our company guideline we are supposed to answer only one question with its 3 subparts. Here…

Q: Without using the ?∞i=1 Ri representation of R+, Prove that for any set relation R (we did not pick…

A: Given: Let us consider the given, R+=∩Q:R⊆Q∧Q is transitive and prove that for any set relation R.

Q: 4. Suppose Rand S are symmetric relations on a set A. Prove that RoS is symmetric iff Ro S = So R.…

A: Suppose R∘S is symmetric Let s, r∈S∘R ⇔r, s∈R∘S⇔s, r∈R∘S ( since R∘S is symmetric)  So, R∘S=S∘R

Q: Let P be a partition of the nonempty set A. For x, y E A, define xQy if and only if there exists CEP…

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Q: 3. Define the relation R on Z by mR, if and only if 2|(m – n). Show that R is an equivalence…

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Q: Suppose A is a set and R is a reflexive and transitive relation on A. Show that the

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Q: A relation R defined on the given set A will satisfy

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Q: A relation \(R\) on a set \(AV) is called anti-symmetric if O (a.b) \in R\) implies ( (b,a) \in R\)…

A: Anti symmetric relation is as follows: If (a, b) and (b,a) lies in R then must be a=b.

Q: Consider the set Q = Z × (Z 10), and the relation fupon Q Defined as: (a, b) ↑ (c, d) + a•d = b•c a)…

A: we shall solve the part (a) only , if you want us to do other parts please resubmit the question…

Q: Define a relation on the set {a, b, c, d} that is 6. (a) irreflexive and transitive, but not…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Consider the relation on the natural numbers N defined as follows: for all x, y e N, xRy if and…

A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

Q: ) Let S = {(x, y) E R × R: y – x is an integer} a) Prove the S is an equivalence relation on R b)…

A: Given, S=x,y∈R×R: y-x is an integer

Q: . Show that every map f : A → B of sets decomposes as hog where g : A → C is surjective and h : C →…

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Q: A relation R, is defined on Z, the set of integers by aRb + a - b is even. Show that R is…

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Q: 1. Suppose R and S are symmetric relations on a set A. Prove that Ros is symmetric if Ros=SOR

A: Given:  To prove R and S are symmetric relations.

Q: Draw the Hasse diagram for the relation C on the set P({1,2,3}).

A: According to the given information, it is required to draw the hasse diagram for the given relation.

Q: Let R be a relation defined on the set Z by aRb if floor value of a = floor value of b. What…

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Q: A relation R on a set A is backwards transitive if, and only if, for every r, y, z E A, if rRy and…

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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 =…

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

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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 =…

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Q: See the instructions for Exercise (19) on page T00 from Section 3,1 (a) Proposition. Let R be a…

A: We use definition for following question

Q: Let A be a set and R be a reflexive relation on A. Prove that R is an equivalence relation if and…

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Q: Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible by…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

A: Given R is a relation from set A to B. Let R is symmetric relation and R-1 be the inverse relation…

Q: A relationR is called a partially ordered set if R is: .a reflexive .b antisymmetric .C transitive…

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Q: Let G={(m,n)∣m,n∈N x N and gcd(m,n)=1}, and define the relation q on G according to (a,b) q…

A: A totally ordered set is a set G together with a relation ≤ that satisfies the following conditions.…

Q: 5. Prove or disprove: for any set A, there exists a relation R on A such that R is both symmetric…

A: Symmetric : If aRb , then bRa , for every a , b∈A Antisymmetric : If aRb and bRa , then a=b

Q: (1) Let A-(a,b,c,d), define a relation R on set A as follows: R-((a,a). (a,b), (b,a), (b,b), (c,c),…

A: Reflexive relation:  A relation R on set X is said to be reflexive if for all elements x∈X we have…

Q: Let R and S be reflexive relations over set A. Prove or disprove that RnS is reflexive

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Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below

Q: 5. Without using the U R representation of R*, Prove that for any set relation R (we did not pick it…

A: We need to Prove that for any set relation R (we did not pick it to be "on" any particular set R+ =…