Complete the definition of on equivalence relation by filling in the two blanks • A reation ~ on a sets is called on equivalence relation if •x ~ y =) yox, for all x, yEs 2 x~y and yz z = for all XIYIZES

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: For each set partition P of each set X, describe the induced equivalence relation (a) X = {a, b, c,…

A: Given, For each set partition P of each set X, describe the induced equivalence relation ~p on X.

Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: How many equivalence relations on A=|42| are there that have distinct equivalence classes of size 4,…

A: Given A=|42| and distinct equivalence classes of sizes 4, 7,7, 8,8, and 8.

Q: Which of these relations on the set {0, 1, 2, 3} are equivalence relations? Determine the…

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Q: Let~ be the equivalence relation on Z defined by a ~ y if and only if x - y is divisible by 5. How…

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Q: We have defined the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…

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Q: Find the smallest equivalence relation (namely an equivalence relation with the fewest number of…

A: Find the smallest equivalence relation such that { (a,b), (a,c), (a,d), (d,e) } is a subset of…

Q: For each of the relations ~ on the integers ~ is relation, explain your an equivalence following…

A: A relation on a set is said to be equivalence relation if it is reflexive, symmetric and transitive

Q: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

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Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: efine the relation ~ on the set N of positive integers by a~b if and only if  a = b(10^k) for some…

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Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

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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: Suppose that the universal set for all variables is Z, and let P(a, b, c) be the predicate a^2 = |b…

A: Given: The universal set for all variables is ℤ. Pa, b, c is a predicate a2=b-c. To provide:  (a) an…

Q: tiv Consider the relation defined on Z by m~n if and only if m+n is eve (a) Show that ~ is an…

A: Consider the relation ~ defined on Z by m~n if and only if m+n is even. Now, To show  Relation ~ is…

Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

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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 equal the set of all strings of O's, 1's, and 2's that have length 4 and for which the sum of…

A: To show R is an equivalence relation, we have to show that R is Reflexive, Symmetric, and…

Q: In each of the following cases of a set X and relation determine whether ~ is reflexive, symmetric,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 7. A relation R on a set X is called an equivalence relation if it is symmetric, reflexive, and…

A: Equivalence relation: A relation R on a set X is called an equivalence relation if it is symmetric,…

Q: count the number of possible equivalence relations on a set of size n by providing a formula in…

A: We use the idea of partitioning to get the total number of equivalence relations.

Q: Consider the set Z of integers and the equivalence relation ~ definel. 2 by a. Ure set- builden…

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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: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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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: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: (Chapter 11.4, #3) The relation relation. Sketch it, by drawing Z as a subset of the line, then…

A: The objective is to show that x≡ymod4 is an equivalence relation. To show the relation is an…

Q: defined are the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…

A: A relation R on a set X is a subset of X×X. That is R⊆X×X. (b). Let ≡6 and ≡10 are two subset on the…

Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

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Q: Let X = {1, 2, 3, 4, 5, 6}. Which of the following could be an equivalence class of an equivalence…

A: Equivalence class on a set

Q: Define a relation R on the set of natural numbers defined by (z, v) E R#z-yis divisible by 3. a)…

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Q: Let - be a relation on a set X defined as below. Determine whether is an equivalence relation on X…

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Q: 7. A binary relation * is defined by the following truth table y x * y F F T T T Which of the…

A: We can make a truth table by considering the options and find which is not equivalent.

Q: Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈…

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Q: 3.3: Is brotherOf an equivalence relation on the set of all people?? How about siblingof?, same…

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