A relation that assigns to each element x from a set of inputs, or ________, exactly one element y in a set of outputs, or ________, is a ________.

Q: In a relation, the set of outputs with respect to a rule is: * O piecewise. range. O domain. O…

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Q: A relation Ron A is an equivalence relation if it is reflexive, symmetric, and transitive. Given: A…

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Q: Give a proof of the following statement. Suppose A, B and C are sets, f is an injective function…

A: We have to prove the given statement.

Q: Questlon In which of the relations represented by the tables below is the output a function of the…

A: To find the relations which shows functions

Q: 2) a) When is a relation R called an equivalence relation? b) Prove that aRb if and only if a = 2*b…

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Q: 1) Define a relation on the set of all people as follows: two persons x and y are related if and…

A: Reflexive: A relation is said to be reflexive, if (a, a) ∈ R, for every a ∈ A. Symmetric: A relation…

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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Q: Let A = {2, 3, 4, 6, 7, 9} and define a relation R on A as follows: For all x, y e A , x R y = 3…

A: Given A = {2,3,4,6,7,9} xRy ⇔ 3 divides (x-y) Therefore 1)  R = (2,2) , (3,3) , (4,4) , (6,6) ,…

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

A: By definition of  relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: Let R be the relationwhose diagraphis given. FInd two cycles of length at least 3 in the relation of…

A: In the given question we have to find two cycles ,whose length is at least 3 in the given diagraph.i…

Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A: (a) A relation is an equivalence relation if it is, reflexive, transitive, and symmetric. Let D be…

Q: Let A= {1,2,3,4,5} and define a binary relation Ramong the subsets of A as follows: XRY XCY. a) Is R…

A: A relation 'R' is defined on set 'A' is said to be: Reflexive : ∀a∈A      aRa Symmetric: if aRb…

Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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Q: 5. Suppose R is a relation on a set A. The inverse relation R-1 is defined by letting a R-1 b if b R…

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Q: - Congressional Representatives Four states were ran- domly selected, and their members in the U.S.…

A: Given   California Florida Illinois Texas Total Democrat 39 10 10 11 70 Republican 14 17 8 25…

Q: Let A = {n| 3 < n S 30} and define a relation on A such that aRb iff a |b. List the relation set R.…

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Q: Let A= {0,1,2,3,4} and a partition of A be: {0,2},{1},{3,4} (a) Write all pairs of the relation…

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Q: Let A = {0,1, 2}. Each of the statements below defines a relation R on A by (m,n) E R if the…

A: A relation between two sets is a set of ordered pairs x,y where x is an element from the first set…

Q: 9.18. Let A = {1,2, 3, 4}. Give an example of a relation on A that is: a. reflexive and symmetric…

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Q: Every function is a relation of its domain and codomain. O True. O False.

A: A relation defined between two sets X and Y contains ordered pair a,b such that  a∈X ,  b∈Y. It…

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

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

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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…

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Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Suppose that P is a unary relation symbol, Q is a binary relation symbol, f is a unary function…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: esentation for each relation. resentation for each relation. berties of each relation.

A: Given:-  S={0,1,2,3,4,5,6} 1] R1=(a,b):a, b∈S, a&gt;b So in…

Q: Determine whether the given binary relation is reflexive, symmetric, transitive, or none of there.…

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Q: Determine whether the relation R on the set of all real numbers is reflexive, symmetric and/or…

A: a) x+y=0 Assume that  A=Set of all real numbers R=x,yx+y=0 The Relation R is not reflexive because…

Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is: %3D (a) reflexive and symmetric…

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Q: Determine whether or not the relation ? on the set of all people is reflexive, symmetric,…

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Q: The relation "is less than or equal to", denoted "S", is NOT an equivalence relation on the set of…

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Q: equivalence relation

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Q: Which of the following relations E are equivalence relations on the set of integers Z? a. xEy if and…

A: Since you have asked question with multiple subparts so as per our guidelines we have to solve the…

Q: 18. Let X be a set. Define a relation R on P(X) by ARB AN B = ) for A, BE P(X). Determine whether…

A: We will use the definition of reflexivity, symmetry and transitivity to check the following :

Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

Q: 1. Let A = {cat,dog,bird,rat} and R be a relation on A defined by {(x,y) : x and y have at least one…

A: We have to solve given problem:

Q: A relation S is an equivalence relation if and only if S is __ symmetric and transitive and…

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Q: 1. Let A = {1, 2, 3, 4, 5, 6}. Write out the relation R that expresses | (divides) on A.

A: The relation R that express |(divides) on A is represented by, R={(x,y)| x,yϵA, x|y}

Q: The domain for a given relation is the set of all integers. Select the correct description of the…

A: we have given a relation that  x and y are related if and only if x and y are both negative or both…

Q: Determine whether or not the relation ? on the set of all people is reflexive,  symmetric,…

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Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A: Given

Q: Let A = {cat, dog, bird, rat} and R be a relation on A defined by {(r, y) : x and y have at least…

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Q: R How to prove that " If is the equivalence B relation on the set and is the function R = IB then

A: given in question R is a equivalence relation on set B that means R is reflexive ,transitive  and…

Q: {cat, dog, bird, rat} and R be a relation on A defined by :x and y have at least one letter in…

A: 2. a. First we now write the relation on A as form of matrix as follows which is also the adjacency…

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

A: We have to determine whether the relation R on the set defined in the parts (a) and (b), are…

Q: Let R be the relation on the set of all mathematicians that contains the ordered pair (a, b) if and…

A: Let R be the relation on the set of all mathematicians that contains the ordered pairs  (a,b) if and…

Q: 14. The number of ordered pairs in the relation R from = {0,1,2,3,4} to B = {0,1,2,3} where (a, b) E…

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