R is the relation defined on Z as follows: m, n € Z, mRn ⇒ 5|(m² – n²). List all the distinct equivalence classes.

Q: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

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Q: The relation R on the set of all integer numbers is defined by R = {(x, y) = Z × Z: x - y ≤ 2} is an…

A: Given a relation R on the set of all integer numbers defined by R={(x, y)∈Z×Z:x-y≤2}.  We have to…

Q: . R is the relation defined on Z as follows: m R n ⇒ 4 | (m² – 1 r (1) Prove that R is an…

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Q: Show that “is unitarily equivalent to” is an equivalence relation on Mn×n(C).

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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: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: for the following relations on 2 the set A = {1, 2, 3}: R = {(1, 1), (1, 2), (1, 3), (3, 3)},…

A: A relation R is an equivalence relation if it is: i) Reflexive: if aRa for all a in A ii) Symmetric:…

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: 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: Consider the relations given below: xRy:x loves y xRy:x2y iii. xRy:x is in the same classroom with y…

A: If x = y and y = x then we can say that relation is symmetric relation.

Q: The domain of relation R is ZxZ. (a, b) is related to (c, d) if a s c and b s d. Which statement…

A: In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and…

Q: (2.3) Prove that R is an equivalence relation.

A: Prove R is an equivalnce relation.

Q: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that  x is congurent to y mod 4.

Q: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: Let T be the relation defined by, For all a, b e Z, aTb iff a – b is odd. Is T an equivalence…

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Q: Please show the following question in detail, I don't understand one bit of it, " Let R be a…

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Q: Problem 2: Relations Define he relation R on N as Ve, deN, (c, d) € R iff e+d is even. (a) Prove…

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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: 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: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

A: Given a relation, aRb⇔ab≤0. To check whether R is an equivalence relation on set ℤ. A relation is an…

Q: Which of the following relations on R are equivalence relations? Z,Q and R stands for set of…

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Q: Let be the relation on True False N defined by R={(n, m) : m³ = n + 1). Then R is one-to-one.

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Q: Decide whether the following relations is an equivalence relation or not. {(x, y) | xy > 0, x and y…

A: The given relation is: R=x,y| xy&gt;0, x,y are integers We know that a relation R on a set X is an…

Q: Let A={1,2,3,4}, B={1,3}, and the relations R1: a <b, R2: a +b = 4

A: A = 1,2,3,4  and  B = 1,3Relation R1=(x,y):x∈A, y∈B and a&lt;b                     =1,3,2,3As (1,1),…

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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