prove why they have or do not have the properties: reflexive, symmetric, antisymmetric, transitive they have. Write which of these is an equivalence relation.  2) Set A = (0,1,2,3), relation R:A x A is defined as: R = {(0,0},(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)}

Q: 8. Define relation R on (Z+ U {0}) × Z+ by (a, b)R(c,d) if ad = bc. (a). Prove that R is an…

A:

Q: If R ={ (1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} is a relation on {1, 2, 3, 4}. Find the reflexive…

A:

Q: 2. The relations below are defined on the set {0,1,2,3}. Determine which of these relations are…

A:

Q: Show that the relation R on ZxZ defined by (a, b) R (c, d) if and only if a + d = b + c is an…

A: To show that the relation R on Z×Z defined by(a, b) R (c, d) if and only if a+ d = b+ c is an…

Q: Let R1 and R2 be the relations on {1,2,3,4} given by R1 = {(1,1), (1,2), (3,4), (4,2)} R2 =…

A:

Q: Let A = {1, 2,3, 4}. The following relation R is an equivalence relation on A: R=…

A:

Q: R={(0,4), (3,0), (3,1), (4,2)}. Find transitive closer of R. Show diagram. A=Z+ x Z+ show relation R…

A: The question involves finding the transitive closure of a relation R and demonstrating the relation…

Q: Let R be the relation on the set (0, 1, 2, 3} and R= {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3,…

A:

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

A: Given that   be a relation on the set Reflexive:  For every…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

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: Plz explain properly.

A: The objective of this question is to find the Cartesian product of sets A and B, the relations R and…

Q: 13. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

A: The relations on 0, 1, 2, 3 are given as: (a) 0, 0, 0, 2, 2, 0, 2, 2, 2, 3, 3, 2, 3, 3 (b) 0, 0, 0,…

Q: prove why they have or do not have the properties: reflexive, symmetric, antisymmetric, transitive…

A: A=a,b,cR=a,a, b,b, c,c, a,b, a,c, c,b A relation R is reflexive if a,a∈R for every element a. Here…

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

A: The objective of the question is to determine which properties - reflexive, symmetric, and…