Consider the set A ={(1, 3), (2, 4), (-4,-8), (3, 9), (1, 5), (3, 6). Define the relation R on A as follows: for all (a, b), (c, d) EA, (a, b) R (c, d) ad bc. a) Draw the directed graph of R. b) Find the equivalence class of (2, 4). (c) Is R antisymmetric?

Q: Draw the directed graph of the relation R = {(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)} X=123 43

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Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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Q: Let A be the set of all triangles defined by R = {(A1, A2) : A1 =A2). Show that R is an equivalence…

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Q: Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: Suppose A be any set and R is relation defined on A. Then R is transitive if whenever (a,b)∈R and…

Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: 2. Define the sets X = {1,2,3} and Y = {4,5,6}. Now, define the relation R from X to Y by „R, if and…

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Q: Let R be a relation from Q to Q defined by R = {(a,b): a,b ∈ Q and a – b ∈ Z}. Show that:(i) (a,a) ∈…

A: i) Given that a ∈ Q  a-a=0 ∈ Z So, (a,a) ∈ R for all a ∈ Q (proved)

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is…

A: Given, relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}.

Q: Assume R is a relation Dver set A. a) prove Ris anti-ceflective 1 Diaw graph G(LE) where the…

A: A relation R on a set X is said to be anti-reflective if no element  of X is related  to itself…

Q: 4. Consider the relation R = {(-3, –3), (-3, –5), (-5, –7), (–7, –3), (–7, –7)} on the set А 3D {-1,…

A: We have to  (a) To Draw Directed Graph.  (b) To find R2=RoR.

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: Q3: Let A = {a, b, c, d} and define relations Ri. R, Rs, and Ri on A, what would be their directed…

A: As per bartleby guidelines for more than three subparts in a question only first three should be…

Q: List the ordered pairs in the relation R from A = 0, 1, 2,3,4, B = 1,2,3, 4, 5, where R is defined…

A: Relation : A relation from a set A to a set B is a subset of A×B. i.e. a relation R consists of…

Q: Define a relation R, on the set A = (0, 1, 2, 3) as follows. R, = {(0, 0), (0, 1), (1, 1), (1, 2),…

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Q: Consider the relation on A = {a, b, c, d, e} given by R ={(a,b),(b,c),(b,d),(b,e),(d,e)} .Explain…

A: Given that, A=a,b,c,d,e And R=(a,b),(b,c),(b,d),(b,e),(d,e) The graph for the diagram is,

Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: Show that the relation R in the set A of all the books in a library of a college,given by R = {(x,…

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Q: Consider the relation R on the set {a,b,c,d,e,f} which is defined as follows: R={(a,a), (a,b),…

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Q: I have almost half of the answers but are what I really need help with is b, c, and d. Thank you…

A: Given,          A=3, 4, 6, 7and define relation R on A as follow;     For every x, y∈A, xRy⇔3|(x-y)

Q: Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a…

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Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Let A={1,2,3,4} and R a relation on A such that A/R={{1},{2},{3,4}}. Then the number of ordered…

A: Given problem is : Let A={1,2,3,4} and R a relation on A such that A/R={{1},{2},{3,4}}. Then the…

Q: Let S {(a,b): a,be R, a 0}. Show that the relation R defined on S by (a, b) R(c,d) if = ad be is an…

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Q: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

Q: Let R be a relation over set A. Let A = {1,2, 3, 4, 5, 6} and let R = {(a, b) e A² : |a – b| > 3} a)…

A: A relation R on a set A which is a subset of  A×A is said to be reflexive if for any x∈A,x,x∈R.  A…

Q: Consider the relation R on R2 given by for any (a,b),(c,d)∈R 2, (a,b)R(c,d) if and only if a 2 +b…

A: According to the given information, Consider a relation R on R2 as:

Q: Let R be the relation on the set of people with doctorates such that (a, b) ER if and only if a was…

A: Let A be the set of all people with doctorates and R be a relations on A defined by a,b∈R if and…

Q: |Given the relation R= {(1,1), (2, 4), (3, 1), (4, 1), (5,2)} on the set A= {1,2,3,4,5), find the…

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence…

A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

Q: Let R be the relation on the set S = {1,2, 3, a, b, c} given by xRy if and only if (x, y) E {(a, a),…

A: S=1,2,3,a,b,c To find: (a) , (b) , (c).

Q: Consider the set Q = Z × (Z 10), and the relation fupon Q Defined as: (a, b) ↑ (c, d) + a•d = b•c a)…

A: we shall solve the part (a) only , if you want us to do other parts please resubmit the question…

Q: Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is…

A: Given, Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) :…

Q: Define a relation S from R to R as follows:…

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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: 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…

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Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

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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: See the instructions for Exercise (19) on page T00 from Section 3,1 (a) Proposition. Let R be a…

A: We use definition for following question

Q: Consider the set Q = Z ×(Z 10), and the relation tupon QDefined as: (a, b) ↑ (c, d) e a·d=b·c a - d…

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

A: A relation R is called reflexive on a set A if (x,x) is in R for all x in A. A relation R' is called…

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: Define a relation R on the set J ={ 0, 1, 3, 4, ,5, 6 } as follows for all x, y E J x R y if and…

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Q: Let A = Z. Define R to be the relation where a~b if ab > 0. Then R is equivalence relation.

A: We have given the set A = { Z : the set of integers }  R= { (a,b) : a,b belongs to Z and a.b >0}…

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: Show that the relation R on Z defined by a R b if and only if 5a − 3b is even, for a, b ∈ Z, is an…

A: Given information: The relation R on Z defined by a relation b if and only if 5a − 3b is even, for…

Q: Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2),…

A: To find the transitive closure of a relation, we just add the ordered pairs that completes the…

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: Let R be the relation on N defined by a R b if either a | 2b or b | 2a. Is R an equivalence…

A: image is attached

Q: I. Draw the directed graph and list the set of ordered pair of R, of the following. 1. If…

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