Let Z be the set of integers. Z = {- 3, - 2, - 1, 0, 1, 2, 3 ...} Let R be an equivalence relation defined on set Z as "“any two elements a and b of Z belongs to R" if a - b = 3m, me Z" %3D Find a partition of Z.

Q: (a) classes of X induced by Prove that - is an equivalence relation on X and describe the set X/ ~…

A: This is a problem of relation.

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: Let  A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all m, n ∈ A,…

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Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b): a is a…

A: Given  Set  = set of all natural numbers N Relation = R = { (a,b) : a is multiple of b }   A…

Q: = {1,2,3,4,5} and define a relation R on S x S by (a, b)R(c,d) if ad = bc. Show that R is an…

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Q: Let Z be the set of integers. Z = (- 3, - 2, - 1, 0, 1, 2, 3 ...} Let R be an equivalence relation…

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Q: SULU Let R be a relation over the integers (Z). Prove that R= {(a,b) : a mod 4 = b mod 4} is an…

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Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

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Q: Let A = {1, 2, 3, 4, ..., 23} and define a relation R on A as follows: For all x, y € A, x R y =…

A: Solution is in next step

Q: {0,1,2,3,4,5,6,7,8,9} by x ~y A x2 = is an equivalence relation on X and identify the equivalence…

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Q: Let Z be the set of all integers. Define relation R on N as follows. Va, be N, (a, b) € R iff i€ Z.=…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

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: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

Q: Let A={ 1, 2, 3, 4, 5} R={ (1,1), (1,2), (2,1), (2,2), (3,3), (3,4), (4,3), (4,4), (5,5) } Write the…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: Given set is A = {1, 2, 3, 4, 5} and relation is R = {(1, 1), (1, 2), (2, 2), (2, 5), (3, 1), (3,…

Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…

A: Consider the given information.

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

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  A = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4}  and define a relation R on A as follows: For all x, y…

A: The set A is defined as: A = {-5, -4, -3, -2, -1, 0, 1, 2, 3 4} x R y ⇔ 3|(x − y). R is an…

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

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Q: Let A = {1, 2, 3, 4, 5, 6} and R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 3), (3, 2)}.…

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Q: Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are…

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Q: be an equivalence relation on the set A = {1, 2,...,8}, and denote the equivalence class of x E A by…

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Q: Suppose A = {-4,-3,–2,–1,0,1,2,3,4} and R is defined on A by aRb a² - b² is divisible by 4. Prove…

A: A relation R on a set A is said to be an equivalence relation, if it satisfies the following three…

Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

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Q: Let A = {a, b, c, d, e} and define an equivalence relation R C A × A on the set A as follows: R =…

A: We will answer the first question as you didn't specify any. Please resubmit the other question…

Q: Let R be the relation on the set {1,2,3,4} containing th (1,2), (1,4), (2,1), (2,2), (2,3), (3,1),…

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Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…

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Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

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Q: Show that the relation R in the set A = {1, 2, 3, 4, 5} given byR = {(a, b) : |a – b| is even}, is…

A: Given that: A = {1, 2, 3, 4, 5} R = { (a,b) ; |a – b| is even}For any element a ∈A, we have |a -a| =…

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: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

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Q: Let A={1,2,3,4,5,6} and let R be the equivalence relation on A defined by…

A: Two elements are in same equivalence class if they have an equivalence relation. Given :…

Q: For non empty binary relation R={(a, a),(a, b),(b, a),(b, b),(c, c),(c, d),(d, c),(d, d)} on the set…

A: We have to solve given problem:

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

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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: Let A = (-2, -1, 0, 1, 2, 3, 4, 5, 6, 7} and define a relation R on A as follows: For all x, y E A,…

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Q: . Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y…

A: Consider the given information:

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…

Q: Theorem. Let < be a preorder on a set X. Define the relation =, where x = y holds if and only if x <…

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Q: 10. Let be the relation defind on Z by „R, if and only if a|b. Orve an explicit description of the…

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Q: Let A = {1,2,3,4} and let R = equivalence relation. Determine the equivalence classes.…

A: Given A=1,2,3,4 and R be the relation defined by R=1,1,1,2,2,1,2,2,3,4,4,3,3,3,4,4. We have to show…

Q: Find the number of different partions of a set (a) with one element (b) with two elements (c)…

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Q: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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Q: Suppose an equivalence relation R has the following equivalence classes that partition the set X.…

A: The ordered pairs in the equivalence relations produced by the given partitions {0, 2}, {1}, {3, 4}.…

Q: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…

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Q: Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are…

A: Given, Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.