Let the relation non z defined by x ny if and only if 3/(x+2y) Show that n is an equivalence relation. Thanky en! ☺

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: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

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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: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given MI conditions are met,…

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Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: PROVE THAT IF A RELATION X ON NON EMPTY SET B IS REFLEXIVE AND TRANSITIVE THEN THE RELATION X…

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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: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

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Q: (b) Let R be the equivalence relation on the set S = {1,3, 5, 7, ..., 49} defined by x Ry if and…

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Q: 1. Let F be a nonempty family of transitive relations. Prove that NF is a transitive relation. Hint.…

A: Given that the F be a nonempty family of transitive relations.

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: Define a relation " on Z by a ~ b if 3a + 4b = 7n for some integer n. Prove that - defines an…

A: A relation ~ on ℤ by a~b if 3a+4b=7n for some integer n.

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

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Q: 1) Let S be the equivalence relation on R defined by xSy iff x-y Q. Then a) [√3]-(-√3+r,req) b)…

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Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

A: Solution:

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: (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: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

Q: Let S' = {x € R² : ||x|| = 1} C X. and endow S' with the same equivalence (b) relation - as above.…

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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…

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Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

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

A: Consider the provide question,

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: 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: 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: ) Let S = {(x, y) E R × R: y – x is an integer} a) Prove the S is an equivalence relation on R b)…

A: Given, S=x,y∈R×R: y-x is an integer

Q: on K³defined by: (a, b, c) ~ (d, e, f) if and only if ak e K – {0} such that (a, b, c) = k(c, e, d)…

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

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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

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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 R be a relation on Z defined by R = {(p, q) E Z × Z |p – q is a multiple of 3}. (a) Show that R…

A: Since you have asked a question having multiple subparts, we will solve the first three subparts for…

Q: The relation defined as x ~ yx ≡ y (mod7) for x, y ∈ Z in Z Write the equivalence classes by writing…

A: Relation R is defined in Z as x≡y(mod 7)  (difference of x and y is multiple of 7) Reflexivity : For…

Q: Let S be the following relation on R\{0}: S = {(x, y) = (R\{0})² : y/x = 2k for some integer k}.…

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Q: 4|(x+3y)

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Q: Define - on Z as follows. Suppose that a ~ b if a² = b² (mod 6). Prove that - is an equivalence…

A: We need to prove 1) Reflexive 2) symmetric 3) transitive.

Q: 2. A relation p is defined on the set of all real numbers R by xpy if and only if |x-yl s y, for x,y…

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Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

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

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Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

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: Let R be the relation on the set of all people who have visited a particular Web page such that x Ry…

A: Given

Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the…

A: Let S be a nonempty set. Consider the relation ~ on P(S)  defined by A~B if A∪Bc=S To show: "~" is…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Q: 1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x²…

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Q: Let the relation R be {(1,2), (2,9), (5,6)}. Is R transitive? Give the reason.

A: Given : 1,2, 2,9, 5,6