Let X = {1,2,...,30} and define binary relations R, S on X as follows. aRb if and only if a = bk for some integer k. aSb if and only if ab = k2 for some integer k. Determine, with justification, whether each of R and S is an equivalence relation. If the relation is an equivalancewrite down the partition of X to which it gives rise.

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: 5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a <…

A: Since you posted a multi sub part question but according to guidelines we will solve first three sub…

Q: 8. Draw the directed graph of the binary relation S on B = { a, b, c, d, e} by S = {(a, b),(b,…

A:

Q: Let R be a relation on the set A = {0, 1, 4, 8} defined by xRy if and only if x + y < 8. (i) List…

A:

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: 1. Prove that the relation "divides" on the integers is reflexive and transitive.

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

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

A:

Q: b) Check whether the relation R on the set S = {1, 2, 3} with the the matrix 1 1 1 0 1 1 1 1 1 is an…

A:

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

A: P={{a,b,d},{c,f},{e,g}} . The  equivalence relation is as follows:…

Q: Let A = {1, 2, 3, 4, 5, 6}, and consider the following equivalence relation on A: R = {(1, 1),  (2,…

A:

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x –…

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

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: Define a relation on Z by x ~ y if and only if x + 2y is divisible by 3. Show that this relation is…

A:

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 A = {1,2,3, 4, 5, 6, 7, 8, 9, 10) and define a relation R on A by a R b if 6. and only if a and…

A: 6. By the definition, a R b iff a and b have the same remainder when divided by 4.     So, obviously…

Q: Define a relation on Q by a b if a-b= for some k, n € Z and n > 0. (i). Prove that it is an…

A:

Q: If S and R are both anti-symmetric, then S∘R is anti-symmetric. (f) If S is anti-symmetric, then…

A:

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

A:

Q: Show that the relation R defined on the set of integers ℤ by (a,b) Î R if a – b = 6k for some k Î ℤ…

A:

Q: Exercise 17.2.18. Find binary relations on {1,2,3} that meet each of the following conditions.…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

A:

Q: Let 4= {1, 2, 3, 4, 5, 6} and the relation R on A is defined by R = {(a,b)|a + b is prime; a, b E A}…

A:

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: Let A = {1,2,3,4}, and let R be a binary relation on A×A given by: ((a, b), (c, d)) ∈ R if and only…

A:

Q: 8. Let A = {1,2,3}. Give an example of a binary relation on A that is a) Reflexive, but neither…

A:

Q: 5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a <…

A: