Let P={{a,b,d},{c,f},{e,g}} be a partition. Write the relation matrix for the implied equivalence relation.

Q: Let A C B and let S be an equivalence relation on B. Prove that R = {(x,y) E A × A : (x, y) E S} %3D…

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Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

Q: Given the following relation, { ( A, A ), ( A, B ), ( A, E ), ( B, B ), ( B, E ), ( C, A ), ( C, B…

A: Given the following relation, {(A, A), (A, B), (A, E), (B, B), (B, E), (C, A), (C, B), (C, C), (C,…

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: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

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Q: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

A: Relation as a Matrix: Let A = {a1,a2,a3,.......am} and B = {b1,b2,b3......bn} are two finite sets,…

Q: . A) Write the ordered pairs, graphical representation, and the relation matrix, for  the Relation R…

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Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: B and let R = {(x, y) E A x A | g(x) = g(v)}. Suppose g: A Show that R is an equivalence relation on…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

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  R = {(x,  y)  iff    x∣ y}  be a relation on set A ={12,3,,5,8,9} Write the relation R in…

A: Since you have asked for a question with multiple sub-parts. We will solve the first three sub parts…

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: Determine whether the relation R is a partial order relation on the set of positive…

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Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

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Q: Given the following adjacency matrix, A, for nodes a, b, c, and d, find the transitive closure of A.…

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Q: Let A= {0,1,2,3,4} and a partition of A be: {0,2},{1},{3,4} (a) Write all pairs of the relation…

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Q: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

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Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

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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: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

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: Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the…

A: Given a relation R on the set B as "is factor of" B=1,2,3,6. a The ordered pair is…

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: Given a natural number c ∈ N. The relation Rc is defined as follows: ∀ a, b ∈ N :  (a, b) ∈ Rc ⇔ (∃…

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Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

Q: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that  x is congurent to y mod 4.

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: Draw the shape of relation z - V3e Зе V3.

A: We are given the relation : z-3eiπ3=3---(1) Now, Let, z=x+iy---(2) Now, 3eiπ3=3cosπ3+i…

Q: Consider the relation R = {(a, a), (c, a), (b, c), (d, b)} then which of the following set…

A: We need to find R3 given R=a,a,c,a,b,c,d,b Now,  R2=RοRR3=RοR2=R2οR The composition of two…

Q: Let X = {1, 2, 3, 4}. Let R = {(1, 3), (2, 1), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (a, b) },…

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Q: a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an…

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Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows:…

A: We have to Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as…

Q: Let A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using…

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

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that R ∪ S is…

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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: 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: Determine whether the following relation is an equivalence relation or not. (a) G = {(x, y) |æ…

A: We have to determine whether the given relation is equivalence relation or not.

Q: Consider the relation R = {(a, 6), (6, 6), (6, c), (c, b), (c, c), (d, a), (d, c), (d, d)} on {a, 6,…

A: Given: R=a,b,b,b,b,c,c,b,c,c,d,a,d,c,d,d (a) Diagraph of R is as follows:

Q: Let P=[[a.b,d).[c.f).le.g]] be a partition. Write the relation matrix for the implied equivalence…

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Q: 2. Given a relation, R on A = {a, b, c, d} on as follows: %3D R = {(a, a), (a, b), (a, d), (b, b),…

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Q: The system represented by the input-output relation, yln]= 2x[n]is an example for a first order…

A: Solve as below

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 A={5,10,15,20, 25} and a partition of A be: {5,25},{10, 20} , {15} (a) Write all pairs of the…

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Q: Which of the following are examples of an equivalence relation on Z? Select all that apply. A. a ~…

A: Hence the relation is an equivalence relation.

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.