M is the relation defined on Z as follows: a M b ⇐⇒ a ≡ b mod 5. (1) Prove that M is an equivalence relation. (2) Find the equivalence classe

Q: Define a relation S on Z as follows: For all integers a and b, aSb ⇔ 7|(a − b). (This relation is…

A: The given problem is to determine whether the relation is reflexive, symmetric and transitive for…

Q: Let A be a nonempty set and let R1 and R2 be equivalence relations on A. For each x E A, describe [x…

A:

Q: = {1,2,3,4,5} and define a relation R on S x S by (a, b)R(c,d) if ad = bc. Show that R is an…

A:

Q: . R is the relation defined on Z as follows: m R n ⇒ 4 | (m² – 1 r (1) Prove that R is an…

A:

Q: Select the following relations on Z that are equivalence relations. O{(a,b)|a>b-1} {(a,b) | a² = 6²…

A:

Q: H 22. D is the relation defined on Z as follows: For all m, n = Z, m Dn ⇒ 3/(m²-n²).

A: A relation S is said to be an equivalence relation on set A if it is reflexive, symmetric and…

Q: Let R be the relation on Z defined by xRy if x² = y² (mod 5). Prove that R is an equivalence…

A: We recall the definition

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 R be a relation over the positive integers defined as follows: R = {(a,b) | 2b < a < 3b }…

A:

Q: A relation R is defined on Z by xRy if and only if 8 divides 3x + 5y. Prove that R is an equivalence…

A: This is a question from relation.

Q: Define a relation R on Z by a R b if a = b + 5k for some integer k. Complete the following…

A:

Q: A. Let R be a relation on set A. A={x : x ∊ J and 0 ≤ x ≤ 12}, and R={(a,b) : |a – b| is multiple of…

A:

Q: Let S = {1;2;3;4}, and suppose that ~ is an equivalence relation on S: You are given the information…

A: Given: S=1, 2, 3, 4 and ~ is an equivalence relation on S. Also we have 1~2 and 2~3. To show: There…

Q: Let R be the relation on the all integers given by xRy iff x- y 2k for some integer k. (1) Prove…

A:

Q: Let S be the following relation on R\{0}: S = {(x, y) = (R\{0})2: y/x = 2k for some integer k}.…

A:

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: Show that each of the following relations equivalence classes. on Z is an equivalence relation, and…

A: In the given question we have to find the equivalence classes.

Q: Let T be the relation defined by, For all a, b e Z, aTb iff a – b is odd. Is T an equivalence…

A:

Q: Define S to be the following relation on R[x]: S = {(f, g) = R [x]²: (x + 1) divides (g - f) in R[x]…

A:

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: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

A:

Q: Define a relation R on the set of all integers Z as follows: for all integers m and n, m R n → m = n…

A:

Q: a. Define a relation Ron Z as follows: For all integers m and n, mRn ⇒ 3|(m − n). Then 3R5 (A) True…

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: 2. Let R be a relation defined on the set of integers Z where a Rb if and only if a? = b° (mod 5).…

A:

Q: Let R be a relation on the set of all integers such that aRb if and only if a + b is even. Is R…

A:

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

A:

Q: Let ~ be the relation on Z defined as follows: For every m, n = Z, 5/(m²-n²). M~ n

A:

Q: Let S be the following relation on R\{0}: S = {(x, y) = (R\{0})² : y/x = 2k for some integer k}.…

A:

Q: 1. Given the binary relation R on R defined by „R, if and only if x > y – 1, for each of the…

A:

Q: A relation R is defined on R by a R b if a – b e Z. Prove that R is an equivalence relation and…

A: