Given the function f= {(n,n²)such thatn< 3,n€N} as a set of ordered pairs in set-builder notation, which set is equivalent to it in list form? O {(0,0), (1,1),(2,4),(3,9)} O {(2,4),(1,1),(3,9)} O {(-1,1),(0,0), (1,1),(2,4),(3,9)} O {(0,0), (1,1),(2,4) }

Q: For each set partition P of each set X, describe the induced equivalence relation (a) X = {a, b, c,…

A: Given, For each set partition P of each set X, describe the induced equivalence relation ~p on X.

Q: Set A is bounded above if and only if set -A is bounded below.

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Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: 4. For every given pairs of sets A and B below, determine whether A = B, or AC B, or BC A, or none…

A: As you post multiple question according to guideline I only have the first three please post the…

Q: {a,b, c, d} which is symmetric and (a) Give an transitive, but not reflexive. example of a relation…

A: a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…

Q: Let A = {0, 1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9}, and C = {0, 2, 4, 6, 8} k. Is {0} ⊆C? l. Find the…

A: K. Yes {0} is a subset of C.  I. Card (C) = 5 Hence card ( P(C)) = 25…

Q: (a) How many one-to-one functions are there from a set with five elements to a set with six…

A: A function f is said to be one-one if ff(x)≠f(y)  if x≠y

Q: 2. Let R be the relation on the set A = (1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) e R if the…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: Show every possible 1-1 correspondence between the following sets. {a, b, c} and {1, 2, 3}.

A: Possible 1-1 correspondence between two sets

Q: Determine the following relation on the set {a, b, c, d}, is reflexive, irreflexive, symmetric,…

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Q: Q. Determine whether the given set V is closed under the operations addition and multiplication…

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Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 7}.    (Enter your answers as…

A: Given ,  U = {x | x ∈ I and −3 ≤ x ≤ 7} We have to find the complement of the set  Let ,  A = {−3,…

Q: (a) How many one-to-one functions are there from a set with four elements to a set with five…

A: A one-to-one function is a type of function that maps each element of the input set to a unique…

Q: Determine whether the given set V is closed under the operations addition and multiplication where V…

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Q: Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R).…

A: Given A be a set and R and S be relations on A. R+S on A is defined by R+S=R-S∪S-R=R∪S-R∩S=R∪S∩R∩Sc…

Q: Find the complement of the set given that    U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.    (Enter your…

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Q: The relation - on the set A = Z x (N - {0}) by (u, v) - (z, w) if and only if wu = zv. Specify the…

A: We will use the relation wu=zv between two elements (u,v) and (z,w) .

Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

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Q: A. Let U= (-∞, ∞) be the universal set and M = [-3,7) and W = [-5,4]. In interval notation,…

A: Given:- A. Let U = (-∞, ∞) be the universal set and M = [-3,7) and W = [-5,4]. In interval notation,…

Q: Let A = {-4, 4, 5, 9} and B = {4, 5} and define relations R and S from A to B as follows: For every…

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Q: Let B be a set and let A ⊆ B be a subset. Suppose that there exists an injective function f : B → A.…

A: Schroder-Bernstein Theorem- Let A and B be arbitrary sets. Using the concept of cardinality. It is…

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

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Q: 5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1,…

A: Let R be the relation on the set 1 , 2 , 3 , 4 , 5 containing the ordered pairs  1 , 1 , 1 , 2 , 1 ,…

Q: Let X = {a} and y = {a, b}, do the following. (a). Use the set-roster notation to write set (X x X)…

A: Define a relation which violate the well define ness

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

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Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B) n (A x C)

A: we have to prove the lemma .

Q: Q. Determine whether the given set V is closed under the operations addition and multiplication…

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Q: 1- Find the set of lower bounds and the set of upper bounds of the following sets in R, if it…

A: Since you have posted multiple sunparts of a question so according to our guidelines we will solve…

Q: Let R be the relation on the set {1, 2, 3, 4} containing the ordered pairs (1, 1), (1, 3), (1, 4),…

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Q: For nonempty sets A, B, and C, |A| <= |B| and |B| <= |C|, then |A| <= |C|.

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

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Q: b) For a set X = {1, 2, 3, 4}, let P be the partition {{1,3}, {2, 4}}. The partition P induces a…

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Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 7}.  (Enter your answers as a…

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Q: Draw the Hasse diagram for the relation C on the set P({1,2,3}).

A: According to the given information, it is required to draw the hasse diagram for the given relation.

Q: Let A = {1,2,3,4}, B = {2,3,4,5}, and C = {2,4,6,8,10}. Suppose R is a 3-ary relation that is…

A: To determine the triples in the array.

Q: Determine if the relation described is an equivalence relation on the given set. Let S = Z+, a ~ b…

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Q: . Draw the Hasse diagram of the relation R on A, where A = (1, 2, 3, 4}, and R = {(1, 1), (1, 2),…

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Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

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Q: 1. List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,…

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

Q: Let X be the set of all sequences (a₁, a2, a3, ...) of real numbers. Define a relation Ton X by (a₁,…

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Q: Give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not symmetric, and…

A: We need to give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not…

Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B)n (A × C)

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Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

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…

A: According to the given information, it is required to check which of the following is true:

Q: Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A…

A: Solution: Let us assume that the subset A has j elements.After fixing A, there are many choices for…

Q: 5. Prove the statement: Let X and Y be two finite sets with |X|=m and |Y|=n. If there is a…

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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: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3)} on the set A = {1,2,3,4,5}.…

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.