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 } . Represent this relation by a matrix. B. Using induction, prove that n2 + n is divisible by 2, where n ∊ N

Q: 8. Consider the binary relation R defined on (N* x N*) by: V (x1. Y1). (X2. Y2) E N* x N*, (x1. Yı)…

A:

Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: Let R be a relation on the set N of positive integers defined by aRb if and only if the product axb…

A: This question is about equivalence  class .

Q: d. Ris a relation on Z* such that (x, y) e R if and only if there is a positive integer n such that…

A:

Q: Let R be the relation defined on P({1, . . . , 100}) by A R B    if and only if |A ∪ B| is even.…

A: Relation on a set

Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (x, y)R(z, w)…

A: We will find out the required values.

Q: If R is a symmetric relation on a set A then a. None O b. mij = 0 for alli %3D O C. mji = 0 for alli…

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: Let S ⊆ N, and for any c, d ∈ N, consider a relation R such that cRd if and only if there exists a ∈…

A:

Q: 3. Let R be the relation defined on Z by aRb if and only if 5 | (4a + b). Prove that R is an…

A: We have given relation on ℤ and defined by  aRb if and only if 5|(4a+b). We can  see here for any…

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 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: let A be the relation on the set integers defined by s A t if and only if |a| <= |t|  is the…

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: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

A: Solution:

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: (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: 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}.…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 3. Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: We are given  that R is a transitive relation on a set A  Transitive Relation  A relation on a set X…

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: 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: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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: et S ⊆ N, and for any a, b ∈ N, consider a relation R such that aRb if and only if there exists c ∈…

A: This is the problem of Relation.

Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A:

Q: Let R be a relation defined on Z as follows: (a,b) is an element of R if and only if the square of a…

A:

Q: Let R be the relation on the set of integers Z defined by m Rn iff m +n = 16. Determine whether R is…

A: Here, relation defined is, mRn iff m+n=16

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: 1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S,…

A:

Q: A relation R on a set A is backwards transitive if, and only if, for every r, y, z E A, if rRy and…

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: Define a relation R on the set J ={ 0, 1, 3, 4, ,5, 6 } as follows for all x, y E J x R y if and…

A:

Q: Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A…

A: Given, A=1,2,3 We can write the above set as, 1,2,3×1,2,3=1,1,,1,2,1,3,2,1,2,2,2,3,3,1,3,2,3,3

Q: Show that the relation R on Z defined by a R b if and only if 5a − 3b is even, for a, b ∈ Z, is an…

A: Given information: The relation R on Z defined by a relation b if and only if 5a − 3b is even, for…

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

A:

Q: Let A={(m,n)∣m,n∈N2 and gcd(m,n)=1}, and define the relation ⪯ on A according to (a,b)⪯(c,d)⇔ad≤bc.…

A:

Q: Determine which of the folowing relations R on Z are oquivaknee relatinns. If R is not an equivakner…

A:

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

A: Relation: - A subset of the productA× B could be a relation R from a non-empty set A to a non-empty…

Q: Let R be the relation on R defined by xRy if there exists some n∈Zsuch that y=x⋅cny=x⋅cn. Let c = 6…

A: This question contains 4 subparts. But according to  Bartleby, only first three subparts can be…

Q: 18. Let R be the relation on R defined by xRy → x – y is an integer. Prove that R is an equivalence…

A:

Q: Let R be a relation on the set of all integers such that a Rb if and only if a +b = 0. (a) Is R…

A:

Q: Let R be a relation on Z. Then R is an equivalence relation if it is defined by xRy if and only if O…

A: A relation R between the elements of a set is said to be equivalence relation if it is: Reflexive…

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: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A: Given: Let A be a non-empty set let~ be a relation on ℘(A) Let "A" be a non-empty set Let ~ be a…

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:

Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

A: