Every equivalence relation is reflexive. True False

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: Write an equivalence relation of Set A = {1,2,3,4,5,6}

A: Set A={1,2,3,4,5,6}

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

A:

Q: Let A = {1, 2, 3}. Then show that the number of relations containing (1, 2)and (2, 3) which are…

A: The smallest reflexive relation on set A containing (1, 2) and (2, 3) is

Q: Prove that the relation of congruence is an equivalence relation.

A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

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Q: is the following relation a functic {(1, 5), (-1, 7), (1, 8), (-4,9)} yes no

A: 1, 5, -1, 7, 1, 8, -4, 9.

Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: PROBLEM1 Instruction: Prove that the relation is  an equivalence relation.  For x, y ∈ R say x is…

A:

Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

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: Suppose R is both an equivalence and partial order relation. Show that every equivalence class of R…

A:

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

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: 11. Prove or disprove: if a relation R is transitive, then R-1 is transitive.

A:

Q: Show that the relation R = ∅ on a nonempty set S is symmetric and transitive, but not reflexive

A: See the attachment.

Q: VIII.3. Is there a mistake in the following proof that any transitive and symmetric relation Ris…

A: Yes there is a mistake. That Symmetric and transitive relation doesn’t imply reflexive. in the…

Q: an equivalence relation c

A: (a) Given, the function                                      id : X→ X     defined by…

Q: Which ONE of the following represents an equivalence relation on the set of integers? Vx.y€Z, xRy if…

A:

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: 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: Show that each of the following relations equivalence classes. on Z is an equivalence relation, and…

A: In the given question we have to find the equivalence classes.

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: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

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: Proving a divisibility relation is transitive

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

A:

Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…

Q: Which of these relations on {0, 1, 2, 3} are equivalence ?relations

A: Equivalence relations are the relations which are reflexive (xRx), symmetric (xRy implies yRx),…

Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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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: Define: what is an equivalence relation?

A:

Q: There are as many equivalence classes as there are which of the following? (Select all that apply.)

A: There are many equivalence classes.

Q: Show that any 1-cut relation (for 1> 0) of a fuzzy equivalence relation results in a crisp…

A: Consider the fuzzy relation: R =10.800.10.20.810.400.900.4100010010.50.20.900.51 Fuzzy tolerance…

Q: 3.3: Is brotherOf an equivalence relation on the set of all people?? How about siblingof?, same…

A:

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

A: Given problem is :

Q: 9.42. Prove or disprove: The union of two equivalence relations a nonempty set is an equivalence…

A: We are asked to prove or disprove, the union of two equivalence relation on a non empty set is an…

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: 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: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

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

A:

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

Q: equivalence

A:

Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…

Q: What is the possible number of reflexive relations on a set of 5 elements?

A: Introduction : We have give a set of 5 elements , we have asked for the number of reflexive…

Q: Define equivalence class and partition of a relation.

A: Define equivalence class and partition of a relation.