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

Q: Let R and S be two equivalence relations on a nonempty set, and T their intersection. What's their…

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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: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

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

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Q: 5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}. Define a relation R on S as follows:…

A: Any Relation is said to be equivalent if  it Reflexive , Symmetric and Transitive

Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

Q: The relation on the set of integers R {(x, y) : 5 divides a- y} is O a. an equivalence relation O b.…

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Q: Define the following terms:  POSETS [ Equivalence relation

A: As two, questions are given , I will solve only the first one. Poset  is referred to as…

Q: Let A be the set of all statement forms in the three variables p, q, and r, and let R be the…

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Q: 4. a) Define the following terms: i) POSETS ii) Equivalence relation

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

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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: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Let A = {a, b, c, d, e, f,g, h}, and let G and H be the following equivalence relations in A: %3D G…

A: Given that A = a , b , c , d , e , f , g , h . Also,  G and H are the following equivalence…

Q: . How many equivalence relations are there on the set S = {1, 2, 3, 4, 5}? 15 45 60 52

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Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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Q: Define the following terms: i) POSETS ii) Equivalence relation define th

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: a. Recall that the set Z of integers is the set of equivalence classes {[(a, 6)] | a, 8 e N}, where…

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Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

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: Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and…

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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: Let A = {0,1, 2} × {0, 1, 2, 3}. We define an equivalence relation R on A by saying that (a, b)R(c,…

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Q: Determine whether the following relations are equivalence relations. For those relations that are…

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Q: Determine whether the following relations are equivalence relations. For those relations that are…

A: Consider the given relation is given as:

Q: Determine whether the following relations are equivalence relations. For those relations that are…

A: As you asked too many questions , I do only first three   a)Let V1 = {(x,y)∈ ℤ x ℤ; x + y is an even…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that R ∪ S is…

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Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is. Chose the correct.(A)…

A: Given,

Q: How many equivalence relations on the set {1, 2, 3}? 1. О З 2. O 6 3. О 5 4. O 4

A: The objective is to find the total equivalence relation on set {1,2,3}.

Q: 3. Let X be a set and S and R equivalence relations on X. Prove or give a concrete counter example…

A: Since you have asked multiple questions, we will solve the first and second question for you. If you…

Q: 4) Suppose R ={(a,b) €Z×Z:b-a is divisible by 3}, show that R is an equivalence relation on Z.…

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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: Determine, with justification, whether the following relations are equivalence relations. If so,…

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Q: Which of these relations on the set of all people are equivalence relations? Determine the…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: Which of the following are equivalence relations? If they are not, which of the axioms fails? a) For…

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Q: '17. Prove or disprove: Let R be an equivalence relation defined on a set A. For any x, y E A,…

A: Given result is: '' Let R be an equivalence relation defined on a set A. For any x,y∈A, either x∩y=∅…

Q: 6. Prove the following statements and provide an illustration to substantiate the proof. a) Let R1…

A: (i), (ii) & (iii) implies R1 intersection R2 is an equivalence relation.

Q: Show that the relation R is an equivalence relation in the set A = { 1, 2, 3, 4, 5 } given by the…

A: Given- Set A={1,2,3,,4,5}. To Show- That the relation R is an equivalence relation in the set A = {…

Q: a) If R and S be two relations from set A to B. Show that (RNS)-¹ = R-¹ S-¹ b) Justify the following…

A: We know that ,  A relation R defined on a set A is called equivalence relation if R satisfies the…

Q: Prove that the following relation is equivalence relations and prepare it in latex: On R, with x∼y…

A: Revision : A relation ~ defined on a set  A is an equivalence relation if and only if it satisfies…

Q: The relation on the set of integers R= {(x,y):5 divides x +y} is O a. none of the choices O b.…

A: Use the relevant definitions.

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: Not reflexive.  Symmetric.  Transitive.  Not Equivalence relation.

Q: Prove or disprove: 1. For any relations R and S, ran(S • R) = ran(S). 2. If R and S are equivalence…

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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: equivalence

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