We say that a set A is numerically equivalent to a set B if there exists a bijective function f : A → B. Let S be a collection of sets, and let R be the relation of numerical equivalence on S. Prove that R is an equivalence relation.

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

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Q: Let A, B, C be sets. Let f : A → B and g : B → C be functions. a) Prove that if f and g are…

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Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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A: Let R be a relation on set A .then SYMMETRIC relation: ANTISYMMETRIC relation: Recall: Identity…

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A: Let R and T be arbitrary equivalence relations on a universal set S. Verify whether R ∩ T, or R ∪…

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Q: Let ~ CX *X be an equivalence relation on a set X. For x EX define x := := {x |x E X} is a partition…

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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: Let A = {1, 2, 3, 4, ..., 22} and define a relation R on A as follows: For all x, y E A, x R y →…

A: Given A=1, 2, 3, 4, …, 22 and for all x,y∈A, xRy⇔4|x-y Hence, the relation R is given by…

Q: Consider the equivalence relation on set A={a,b,c} given by R = {(a,a),(b,b),(c,c),(a,b),(b,c)} . s…

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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: 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 C be a relation defined on the set of all geometric polygons, defined by any two polygons in the…

A: The given problem is from relation on sets. Here. Give that C be a relation defined on the set of…

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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: 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: Let R be a relation defined on Z as follows: (a,b) is an element of R if and only if the square of a…

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A: The explanation of the answer is belowExplanation:Step 1: Step 2: Step 3: Step 4:

Q: Let A, B, and C be sets. Prove or disprove: If R and S are equivalence relations on A, then S o R is…

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Q: (b) Let {A₁, A2,...} be a partition of a set X, and R the relation {(x, y) = X²: there exists j such…

A: An equivalence relation is a binary relation between two elements of a set that satisfies three…

Q: Côñšidéř thé rélátión S on the set {a, 0, C} given by S = { (a, a), (a, b), (b, a), (b, b), (c, c),…

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Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…

Q: Let X be the set of all subsets of ℤ . Define a relation R on X as follows: Given two subsets of…

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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: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…

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Q: prove why they have or do not have the properties: reflexive, symmetric, antisymmetric, transitive…

A: A=a,b,cR=a,a, b,b, c,c, a,b, a,c, c,b A relation R is reflexive if a,a∈R for every element a. Here…