Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must consists of at least 4 subsets? Show that this relation is an equivalence relation? Also draw the digraph for this relation?

Q: c) For a set X = {1,2,3, 4, 5}, let P be the partition {{1,3, 4}, {2}, {5}}. In the equivalence…

A: Q1(c) asked and answered.

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

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Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

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

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

Q: On the set A = {a, b, c, d, e, f, g, h} is given by the relation R = {(a; b), (a; c), (a; d), (a;…

A: The set is A=a, b, c, d, e, f, g, h and the relation is R=a; b, a; c, a; d, a; e, b; f, c; f, d; g,…

Q: Given a set define a relation induced by a partition of set A and that partition must consists of at…

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Q: Let R be the equivalence relation on the set A ={ a, b, c, d } induced by the partition ( {a,b,c};…

A: Given A=a, b, c ,dpartitiona,b,c; d

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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Q: 8. Let S = {(a, b), (b, a), (b, d), (b, e), (b, f), (c, c), (d, e), (f,c), (f, f)} be a relation on…

A: INTRODUCTION: A set of ordered pairs is a pair of components that appear in a specific order and are…

Q: Draw the direction of the graph that represents the relations.

A: We need to draw the directed graph which is represented by the given relation,…

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: Given the sets A = {a, b, c, d}, B = {0, 1, 2, 3} construct a relation R such that R is an injective…

A: There are two question , one is related to relation and function , second is related to equivalence…

Q: If S is a relation from a non-empty set A to a nonempty set B then

A: Solution :-

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: Recall that, for any set A, the power set of A, P ( A ), is the set of all subsets of A. Consider…

A: To  find if the inclusion relation on P(A) has the properties of reflexivity, symmetry and…

Q: Let R={ (a,a). (a,b). (b.b). (b,a). (CC). (d,d), (e,e), (f,f). (d,e), (e,d). (e,f), (f.e). (d.f).…

A: Given:  R = (a, a), (a, b), (b, b), (b, a), (c, c), (d, d), (e, e), (f, f), (d, e), (e, d), (e, f),…

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} and R= { (a,a), (a, c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. draw a…

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Q: Let R = { ( a, b ), ( a, d ), ( b, d ), ( c, a ), ( c, c ), ( d, b ), ( d, c ) } be a relation on…

A: Given: R=a,b,a,d,b,d,c,a,c,c,d,b,d,c   The relation R2 contains all ordered pairs (x, z) if (x, y)…

Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. Construct a…

A: The set A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} R={(1,1), (3,1), (2,1),…

Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

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Q: A relation that assigns to each element x from a set of inputs, or ________, exactly one element y…

A: To fill: The blanks of statement: Given: The statement is "A relation that assigns to each element x…

Q: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

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: Let  A = {−6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4}  and define a relation R on A as follows: For all…

A: Concept Used:- In Roster Form All the elements of a set are listed inside curly brackets { } and the…

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

A: Here given that the set is A = {a, b, c, d} and the relation on A is given by R = {(a, c), (b, b),…

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: Determine whether or not the following relations are equivalence relations on the given set. If the…

A: Let m, n, p∈ℚ Relation is m~n in ℚ if mn≥0 (i) Reflexive: Let m∈ℚ then mm=m2≥0 Therefore m~m   ∀m∈ℚ…

Q: (a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

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Q: Let A = {a, b, c, d}, and R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} be a…

A: A = {a, b, c, d} R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} Equivalence…

Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

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Q: Consider the subset relation C on the power set of {a,b,c}, that is P{a,b,c}. (a) Construct the…

A: Let S be a partially ordered set. Use the following definitions, to obtain the solution. Let a,b∈S…

Q: Subject: Set Theory

A: • Transitive relation means that, whenever an element a is related to an element b and b is related…

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

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Q: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

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Q: Let A # 0 be a set. Prove that A? is an equivalence relation on A.

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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: Given the relation R on the set of all integers defined by the rule (x, y) ER if and only if x 2 y².…

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Q: Exercise 3.2. Consider the relation "is a subset of" symbolized C on the collection of all subsets…

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Q: Let S be a set. A subset R CS×S is called a circular relation if (i) for each a E S, (a, a) E R and…

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Q: Let A = {a, b, c, d}, and R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} be a…

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Q: given the relation R define = (0,0), (0, 1), (0, 3), (1, 1), (1,0), (2, 3), (3, 3) on the set A = 0,…

A: Given that  R=0,0,0,1,0.3,1,1,1,0,2,3,3,3A=0,1,2,3 To draw the directed graph and determine whether…

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: 1. Let A = {a, b, c} and B = {r,s, t, u}. Furthermore, let R = {(a, s), (a, t)}, (b, t) be a…

A: Suppose A and B are non empty sets. Define a relation R:A->B then, Domain of R={x: (x,y) belongs…

Q: (1) Let A-(a,b,c,d), define a relation R on set A as follows: R-((a,a). (a,b), (b,a), (b,b), (c,c),…

A: Reflexive relation:  A relation R on set X is said to be reflexive if for all elements x∈X we have…

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

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

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Q: Prove that the given relation is an equivalence relation, and describe the distinct equivalence…

A: Let A is the set of all students at your college. For every x,y∈A,  xSy⇔x is the same age as y. That…