Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the relation an equivalence relation? Explain. If yes, identify (no need to justify) the equivalence class of Ø'

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b): a < b?.…

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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 N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b): a is a…

A: Given  Set  = set of all natural numbers N Relation = R = { (a,b) : a is multiple of b }   A…

Q: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given MI conditions are met,…

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Q: 4. Suppose R is a relation on a set A. The complementary relation R is defined by letting a R b if a…

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

A: Given set is A = {a, b, c, d} and the relation R on set A is R = {(a, b), (b, b), (b, c), (c, 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: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given conditions are met,…

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

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Q: A relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

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Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: let A be the relation on the set integers defined by s A t if and only if |a| <= |t|  is the…

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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: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R?  Note: Select the order that…

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Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…

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

A: Consider the provide question,

Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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Q: Define the relation ~ on the set R of real numbers by x~y if and only if x = -y. Show that ~ is not…

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

A: Let R represent a relation on a given set S=a,b,c,d. Then, relation R is said to be reflexive; if…

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

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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: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

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Q: Define a relation Q on the set Rx Ras follows. For all ardered pairs (w, x) and (y, z) in Rx R, (w,…

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Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

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Q: A relation R, is defined on Z, the set of integers by aRb + a - b is even. Show that R is…

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Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

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Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Let R be a relation defined on the set Z by aRb if floor value of a = floor value of b. What…

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Q: Let R be a relation on Z defined by R = {(p, q) E Z × Z |p – q is a multiple of 3}. (a) Show that R…

A: Since you have asked a question having multiple subparts, we will solve the first three subparts for…

Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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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: Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not…

A: Denote R by the relation on the set S={a, b, c, d} that is irreflexive, symmetric and not…

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: Let R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

A: Given R is a relation from set A to B. Let R is symmetric relation and R-1 be the inverse relation…

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 a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: Theorem. Let < be a preorder on a set X. Define the relation =, where x = y holds if and only if x <…

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Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5} If the relation is…

A: To find: (i)the given relation is equivalence or not.             (ii) The equivalence class.

Q: Let R be an equivalence relation on A. Find the maximum number of classes R can make if JA| = 80 and…

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Q: Suppose R is a relation defined on the set A = {1, 2, 3}. If R = {(1,1), (1, 2), (2, 1), (2, 2), (3,…

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Q: Let R be the relation on the set of all people who have visited a particular Web page such that x Ry…

A: Given

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

A: Concept:

Q: equivalence

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Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A: Given: Let A be a non-empty set let~ be a relation on ℘(A) Let "A" be a non-empty set Let ~ be a…