14. a. Let R be the relation of congruence modulo 3. Which of the following equivalence classes are equal? [7], [-4], [-6], [17], [4], [27], [19] b. Let R be the relation of congruence modulo 7. Which of the following equivalence classes are equal? [35], [3], [-7], [12], [0], [-2], [17]

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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Q: Construct the Hasse diagram for the “divides” relation, | on the set {2, 3, 4, 6, 8, 9, 12, 18}.…

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Q: Let A = {a,b, c, d, e, ƒ}, and let G and H be the following equivalence relations in A: G = IA U…

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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. In the diagram below, there are 9 points and 8 lines: (a) Let be the relation between the points…

A: Given, In the diagram below, there are 9 points and 8 lines. a) Let ⋄ be the relation between the…

Q: . The relation ⋆ means “this number written out in English has this many letters”. For example, 6 ⋆…

A: A relation R  on a set A is said to (1) Reflexive : forall x in A implies (x,x) in R . (2)…

Q: Given the relation R = {(1,2),(2,3)} on the set A = {1,2,3} . What is the minimum  number of ordered…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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Q: Determine whether the relation R on A is an equivalence relation and provide your reasoning: а.…

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Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: 4. Which is the inverse of the relation {(-2,5), (-1,3), (0,-1), (1,-3), (2,-5), (3,-7)}? O {(5,-2),…

A: To find inverse of the given relation.

Q: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

A: According to the given information, Let S be the set of all cars sold in the period 2015 to 2020.…

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

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Q: d) ((f g)| for some CEZ, for all xE Z, f(x) – g(x) = C} e) {f, 8) | f(0) = g(1) and f(1) = g(0)}

A: Part (d) From the given information: The relation is . Here, C is constant.

Q: Which relation has a domain of (3, 5, 8} ? O(2.8). (1. 3), (3, 5)} O(3, 8). (5. 3). (3, 5)} O (3.…

A: Domain of relation: The set containing all the first elements of all the ordered pairs of relation R…

Q: Let A = {1,2,3, 4} and B = {a, b, c, d, e}. How many different relations are there from A to B. Why?

A: Given A=1,2,3,4B=a,b,c,d,e

Q: II. Identify the correspondence in the following relations 8 3 1.) 5 2.) 5 4 3 4 8 8 4.) -2 -3 -4 -5…

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Q: The number of relations on the set A = {1, 2} is 256 . O True False

A: Number of relation with n elements 2n2

Q: Give examples: For each of the four relations between natural numbers x and y in the left column of…

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Q: For the set A = {2, 3, 4, 5, 6, 7, 8), relation R defined by R = {(x,y) = AxA | x divides y} Answer…

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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: Let A = {-9, -7, -6, -4, -3, 1, 3, 4, 8, 10} and B = {-7, -6, -4, 1, 4, 8, 10}. How many sets of C…

A: Given that C has a property thatfrom the second condition we can conclude that all the elements of B…

Q: Let A = {1, 2, 3, 4} and B = {a, b, c, d, e}. How many different relations are there from A to B.…

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