Define a relation " on Z by a ~ b if 3a + 4b = 7n for some integer n. Prove that - defines an equivalence relation. a. b. Find the equivalence class of 0.

Q: Fix a set X, and let S be a collection of equivalence relations on X. Is s U an equivalence relation…

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Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1, 2} defined by (a, b)S(c, d) if and…

A: S=0,1,2,3×0,1,2=0,0;0,1;0,21.0;1,1;1,22.0;2,1;2,23.0;3,1;3,2

Q: Consider the relation K on N defined by Knm iff n <m.Which statement below is true? K is an…

A: It is Irreflexive.

Q: Let R be the relation consisting of all pairs (x, y) such that x and y are strings of uppercase and…

A: Let R be a relation on a set A R is an equivalence relation if it is reflexive, symmetric,…

Q: Let S be the equivalence relation on {− 1, 0, 1} × {0, 1, 2, 3} defined by (a, b )S(c, d) if and…

A: Let A  = {-1,0,1}×{0,1,2,3}  i.e A=…

Q: 9.24. Let R be an equivalence relation on A = {a, b, c, d, e, f,g} such that a Rc, c Rd, d Rg and b…

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Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: . Define r on the power set of {1,2, 3} by ArB → |A| = |B|. Prove that r is an quivalence relation.…

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Q: Let R be the relation on A × A , where A= {1,2,3,4} that is elements of this relation are pairs of…

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Q: Define the relation on the set Z of integers by if and only if a ~b if and only if a = b + 5k for…

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Q: Let R be the relation on the all integers given by xRy iff x- y 2k for some integer k. (1) Prove…

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Q: 2. Define the relation on S = Z by a~b + a = b mod 5. (1) Prove that is an equivalence relation. (2)…

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Q: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

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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: Prove that the following relations are equivalence relation: On Z× (Z−{0}), with (a,b)∼(c,d) if…

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Q: Let D be the binary relation defined below. For all u, w e 2, u D w → w=u +7 or w= u - 7. Show…

A: Solution of given problem is as below: A binary relation is equivalance relation if it satisfies the…

Q: Show that if R and R2 are equivalence relations on A, then R1 n R2 is an equivalence relation on A.

A: Equivalence relation on a set A

Q: Subject: Set Theory

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Q: Define a relation R on Z by declaring that xRy if and only if x^2 ≡ y^2 (mod 3). (a) Prove that R…

A: (a) for any x in Z,       obviously xRx, as x2 = x2 mod 3       Hence, R is reflexive.        If…

Q: 2. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

A: Let A be a non-empty set. A relation R on A is said to be equivalence relation if it is reflexive…

Q: 6. Consider the relation R on Z defined by xRy iff x – y= 4n for some n Ɛ Z. (a) Show that R is an…

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Q: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Define a relation on Z by a R b if a² = b². a. Prove that R is an equivalence relation. b. Describe…

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Q: Show that the relation R defined on the set of integers ℤ by (a,b) Î R if a – b = 6k for some k Î ℤ…

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Q: Let R be the relation on A × A, where A = {1,2,3,4}, that is, ele- ments of this relation are pairs…

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Q: 3. Let R be a relation defined on Q by: Ga) ER if ad = bc a) Show that R is an equivalence relation…

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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Q: Let R be the relation on the set of natural numbers given by the following rule: (n,m) ∈R if and…

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Q: Show that the relation R on Z defined by aRb if and only if 5a−3b is even, for a, b ∈ Z, is an…

A: Let R be a relation from a set A to itself. R is said to be an equivalence relation if 1) R is…

Q: Let S be a set of distinct symbols. Show that the relation defined onW(S) in this chapter is an…

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Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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Q: Let R be an equivalence relation on A - {a,b,c,d) such that a Rc and bRd How many distinct…

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Q: let R be an equivalence relation and let [x] be the equivalence class of x, prove x belong to [x]

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Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Let us consider the following relation R on the set of all pairs of integers: (a,b)R(c,d) if a = c…

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Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: #1. Let R be the relation defined on the set of all integers Z as follows: for all integers m and n,…

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Q: 14. For a,b E Z, define a ~ b if and only if 4a + b is a multiple of 5. Show that defines an…

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Q: 5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence…

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Q: Let R be an equivalence relation on A. Find the maximum number of classes R can make if JA| = 80 and…

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Q: #2. Let S be the set of all strings of O's and 1's of length 3. Define a relation R on S as follows:…

A: Given is a set S of strings.   Also, given a relation R of set S.   To Prove: R is an equivalence…

Q: - Let and x be relations on Z defined as follows: For a, be Z, a~b if and only if 2 divides a +b. •…

A: According to the given information, it is required to solve the question 10.

Q: Define a relation R on the integers Z saying that (m, n) is in R if m2 is equivalent to n2 (mod 7).…

A: First to prove the relation, R, on set of integers Z is equivalence relation. R is defined as:

Q: Show that the relation R defined on the set of integers ℤ by (a,b) ∈ R if a – b = 6k for some k ∈ ℤ…

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Q: equivalence

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Q: Let R be the relation on N defined by a R b if either a | 2b or b | 2a. Is R an equivalence…

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Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ER…

A: A ={ (a,b) : where a and b are positive integers}  R= {(a,b) and (c,d) : a+d= b+c }  We have to…

Q: 8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d)…

A: Equivalence relation