Prove that if R is an equivalence relation on a set A, then the inverse relation R−1 is an equivalence relation on A. step by step please

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  <=> w1 and w2 have a letter in common.  Now, it is obvious…

Q: (a) Give an example of a relation on the set {a, b, c, d] which is symmetric and transitive, but not…

A: (a) Given set is: a, b, c, d. To Do: We have to give an example of a relation on the given set a, b,…

Q: {a,b, c, d} which is symmetric and (a) Give an transitive, but not reflexive. example of a relation…

A: a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…

Q: Let~ be the equivalence relation on Z defined by ~y if and only if z Give three examples of elements…

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Q: Let A be a set. Define a relation over ℘(A) by X ~ Y iff there exists a bijection f: X ⟶Y. Proof…

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Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Let F be a nonempty family of transitive relations. Prove that intersection F is a transitive…

A: Given F be a nonempty family of transitive relations. We have to prove that the intersection F is a…

Q: Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R).…

A: Given A be a set and R and S be relations on A. R+S on A is defined by R+S=R-S∪S-R=R∪S-R∩S=R∪S∩R∩Sc…

Q: Suppose R, S are equivalence relations on set A. Prove or disprove that (a) R-¹nS is also an…

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Q: Show that the intersection of any collection of equivalence relations over a set A is also an…

A: We have to prove intersection of equivalence relations on a set is equivalence Let us suppose R and…

Q: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

Q: set {(a,b),(a, a), (c, a), (b, b)} (a). Let X = {a,b,c} be sets. is a relation on X and find its…

A: Answer and explanation is given below..

Q: Let R be a reflexive and transitive relation on A. Show that RN R¯' is an equivalence relation -1 on…

A: First let, A= set of integers. Then, let, R={(a,b):a,b in A} so,

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Let A = {1,2,3, 4, 5, 6, 7, 8, 9, 10) and define a relation R on A by a R b if 6. and only if a and…

A: 6. By the definition, a R b iff a and b have the same remainder when divided by 4.     So, obviously…

Q: Let R be a relation defined on the set of integers as follows: a R b iff 6 divides  (a - b). R is…

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Q: Let be the equivalence relation on Z defined by z~ y if and only if z-y is divisible by 15. Give…

A: Equivalence relation

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

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Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

A: Definition (Equivalence relation): A relation R is said to be an equivalence relation on a set A if…

Q: (a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

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Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

A: We take the help of the signum function

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: = Give an example of an equivalence relation R on the set A {a, b, c, d, e, f, g, h} such that there…

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Q: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3) and define a relation R on A as follows: For all x, y…

A: Given : A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and R is an equivalence relation on A defines as ;…

Q: Check if the following statement is TRUE or FALSE. Let R be the relation on R² defined by…

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Q: Understanding How the Graphs of Parabolas are Related to Their Quadratic Functions Write the…

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Q: Let A = {1, 2, 3,4, 5, 6} and let R be an equivalence relation on A.  Suppose that 1R2, 3R5 and 6R3.…

A: Given that A = {1, 2, 3, 4, 5, 6} R as equivalence relation on A Given conditions: 1 R 2, 3 R 5, 6 R…

Q: 4|(x+3y)

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