A. Let R be a relation on set A. A={x: xeJ and 0 sxs 12), and R-{(a,b) : la - b| is multiple of 6}. Represent this relation by a matrix. B Using induction provo that 4n 1 in

Q: 4. Consider the following binary relation p on the plane R² (x, y)p(u, v) if y? – a² = v² – u².…

A:

Q: ) Let R = {(a,b) : 3keza = k * b} be a relation over the positive integers. Prove or disprove that R…

A: Given that R=(a,b):a=k*b To show reflexive it is enough to show that a~a. It is true because, a=1*a.…

Q: 2) Let R be binary relation on N defined by r Ry if and only if r <y< 2r. Is R reflexive? Is R…

A:

Q: Let A= {1, 2, 3, 4} and let the relation R on A be defined by the matrix [1110 0101 MR then which of…

A: Given that A=1,2,3,4. The adjacency matrix of the vertices in A is given by the relation R as…

Q: Let R= {(a, b): 3keza k* b} be a relation over the positive integers. Prove or disprove thatR is a…

A: A relation R is partial order relation if R is reflexive, antisymmetric and transitive.

Q: Let A = {2, 4, 5}, and let R be the relation on A consisting of pairs of the form (a, b), where ab…

A: Pairs in R is: {(4,4),(4,5),(5,4),(5,5)} Only these have ab&gt;12

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: Determine whether the following statements are True or False: - Part A: Suppose R1 and R2 are…

A:

Q: let R be the relation on the set A = {1, 2, 3, 4, 5, 6} defined by a R bif and only if a = 2b.

A:

Q: a) A computer program consists of five modules M1, M2, M3, M4, and M5. A relation R on the set of…

A: From the relation matrix for R we observe that…

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…

A: Since not particular question asked ,as per guidelines solution to only first question (i.e A) is…

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: 3. Let R be the relation defined on P({1,..., 100}) by ARB if and only if |AU B| is even. Is R…

A:

Q: Which of the following is/are true for the relation R, where a is related to b (aRb), if and only if…

A: Suppose, A be any set and suppose R:A-&gt;A is a relation. Then, R is reflexive: if for every x in…

Q: a Define a relation R on N by (a,b) e Rif and only if EN Which of the following properties does R…

A:

Q: (b) Let - be the relation on C defined by z ~ w if and only if z + w e R. Proye that is an…

A: This can be solved as follows:

Q: 4 - Let R be the relation on {a, b, c, d} defined by the following matrix. R is reflexive ? 1 0 1 0…

A:

Q: Let S be the following relation on C\{0}: S = {(x, y) = (C\{0})² : y/x is real}. Prove that S is an…

A:

Q: Let A = {1,2, 3, 4, 5,6} and R a relation on A whose MR is given below 0 100 0 1] 0 0 10 0 0 00 1 10…

A: Let R be a relation on a set A. The relation R can be represented using the matrix and the digraph.…

Q: a. Define a relation R on Z as follows: For all integers m and n, mRn + 3|(m – n). Then 3R5 (A) True…

A: We have to check whether given statement is true or false.

Q: Let A = {1, 2, 3, 4} and R a relation on A whose matri: 1 0 1 0 0 1 0 1 is Mr = 0 0 1 1 0 0 1…

A:

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

A:

Q: (2) Let R be binary relation on N defined by rRy if and only if r <y< 2r. Is R reflexive? Is R…

A: We have given that R be a binary relation on ℕdefined by xRy if and only if x≤y≤2x. Now we have to…

Q: Let A = {1,2,3,4} and R a relation on A whose matrix [1 0 1 1 0 1 is MR 1 0 1 1 1 1 1 Determine…

A:

Q: Suppose that each of R ad T is a relation on a set A, the matrix for R is MB, and he matrix for T is…

A:

Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

A:

Q: The matrix representation for the relation R on {v1, v2, v3, v4} is given below. The first…

A: We will use the concept of adjacency matrix to write the ordered pairs of the given matrix

Q: Define the following sets e and s as follows: e = {Devin, Elsa, Floyd}, s = {Software 1, Software 2,…

A:

Q: Let A = {1,2, 3,4} and R a relation on A whose matrix is MR = [1 0 1 1 %3D 0 10 1 0 0 1 0 10 1 1 1…

A: Given-  A=1,2,3,4 Relation R on A whose matrix is MR=1011010100101011

Q: Define a relation R on Z as follows: For all integers m and n, mRn → 3|(m – n). Then 3R5 Α. True B.…

A: Solution:-

Q: A. Let R be a relation on set A. A={x:xeJ and 0 SxS 12), and R={(a,b): a-b is multiple of 2)…

A:

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

A: As this is the multiple question type, only first question is to be solved according to the Bartleby…

Q: Given X = {1,3,5}. R is a relation on X, defined by aR,b if and only if la – bl is an even integer.…

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

A:

Q: t R be the relation on the set of ordered pairs of positive integers ch that ((a,b), (c,d)) e R if…

A:

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: Let R be a relation on the set A = {a, b, c, d} described by the matrix MR=(1 0 0 1          0 1 0…

A: We will use the given matrix to write R in the ordered pair form and then we will find domain and…

Q: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. Let R and T be relations from A to B with…

A: Let A=a1,a2,...,am and B=b1,b2,..,bn Let R:A→B and T:A→B are two relations. Let m and n be their…

Q: Let A = {1,2, 3,4} and R a relation on A whose matrix 1 1 1 1 1 1 is Mr = 1 1 1 1 1 Determine…

A:

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 =…

A:

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 &gt;0}…

Q: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

A:

Q: 5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence…

A:

Q: Let R3 be the relation on Z+ such that xR3y if and only if 2x – 3y > 0. (Recall that Z+ = {1,2,3, 4,…

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 4…

A:

Q: In this exercise, you want to show that a relation RC A? is transitive + R" C R for all n EN=…

A:

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: (a) Let R be the relation on Z defined as follows: For a, b e Z, a~b if and only if a is a multiple…

A: