Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric, anti-symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. This is not a formal proof, but briefly explain your reasoning. [y]}, that is, x and y round up to the sane number. Characterize R in

Q: Congruent is. Relation on Z Equivalence. anti symmetric anti reflexive Equivalence partial order

A: To solve the following problem by using the definition of equivalence relation

Q: For each of the following relations explain if it is: Reflexive, Irreflexive, or neither…

A: As per bartleby guidelines for more than three subparts in a question only first three should be…

Q: 3. Prove that if a reflexive R (on some set A) satisfies x Ry A xRz → yRz (1) for all x, y, z, then…

A: the relation is equivalence if it is reflexive, symmetric and transitive.  the relation is…

Q: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

A:

Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: Consider the equivalence relation on R defined by r ~ y if x – y € Z. Describe the quotient space…

A: In topology and related areas of mathematics, the quotient space of a topological space under a…

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: 1. Let F be a nonempty family of transitive relations. Prove that NF is a transitive relation. Hint.…

A: Given that the F be a nonempty family of transitive relations.

Q: A relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

A: We know that

Q: Prove that "is similar to" is an equivalence relation on Mnxn(F ).

A: We have to prove that “is similar to” is an equivalence relation on Mnxn(F ) i) Every matrix A is…

Q: Let R be a reflexive relation on A. Show that R" is reflexive for all positive integers n.

A:

Q: 5. Let A=Z and R, ={(x,y):x-y is divisible by 5} be a relation on A . That is x R,y if and only if…

A:

Q: 1. Given an arbitrary relation R, suppose we compute two new celations: - R1, the reflexive closure…

A: The solution is given below

Q: Let D be the relation on the natural numbers defined by the rule m divides n if and only if m does…

A: Let D be the relation on the natural number is defined by the rule m divides n if an only if m does…

Q: Let Q be the set of all rational .numbers a) If T= {0}U{ACQ: Q-A isfinite} prove that (Q, 7) is…

A: For the solution follow the next steps.

Q: (1) Define relation R on the real numbers, R, by xRy if and only if [x] = [y]. Determine which of…

A:

Q: For the points (x1, y1) and (x2, y2) in the plane R?let (x1, y1)~ (x2,Y2) mean that xỉ + yỉ = x + y…

A:

Q: 6. Consider the relation R on Z defined by xRy iff x – y= 4n for some n Ɛ Z. (a) Show that R is an…

A:

Q: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Define the relation∼ on Nby m ∼ n if and only if the sum of the distinct primes that divide m is the…

A: To test if the given relation satisfies the conditions for reflexivity, symmetry and transitivity

Q: Let R be the relation on A × A, where A = {1,2,3,4}, that is, ele- ments of this relation are pairs…

A:

Q: Check if the following statement is TRUE or FALSE. Let f be the relation from N to N5 defined byf =…

A:

Q: Let R be the relation on the set of natural numbers given by the following rule: (n,m) ∈R if and…

A:

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

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: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: Prove that the following statement is true for all real numbers x, y ≠ -1, by using a sequence of…

A: y= 1-x/1+x iff x=1-y/1+y proved

Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: The relation "is less than or equal to", denoted "S", is NOT an equivalence relation on the set of…

A:

Q: Let S {3k : k E Z} be the set of integer multiples of 3. Let R be a relation defined on Q by x Ry if…

A:

Q: Consider the set Q = Z ×(Z 10), and the relation tupon QDefined as: (a, b) ↑ (c, d) a•d = b•c d)…

A: Answer is mentioned below

Q: Determine whether the relation R on the set of all integers defined by the rule (x,y) Î R if and…

A:

Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

A:

Q: 4) Suppose R ={(a,b) €Z×Z:b-a is divisible by 3}, show that R is an equivalence relation on Z.…

A:

Q: The relation defined as x ~ yx ≡ y (mod7) for x, y ∈ Z in Z Write the equivalence classes by writing…

A: Relation R is defined in Z as x≡y(mod 7)  (difference of x and y is multiple of 7) Reflexivity : For…

Q: 1 Recall that for x, y ≤ R, |x − y| ≤ Rf is the absolute value of x - y. That is, if x-y≥0 |x - y =…

A: Please see the below picture for detailed solution.

Q: Congruent is.. Relation on Z Equivalence. anti reflexive anti symmetric Equivalence partial order

A: Here we choose the correct option.

Q: Prove or disprove if the composition of surjective relations is surjective. If it is not true, find…

A:

Q: Let RC R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given problem is :

Q: 13. Let R C R XR with {(x, y)|x2 =, y?}. Characterize R in terms of whether it is reflexive,…

A:

Q: Prove that the following relation is equivalence relations and prepare it in latex: On R, with x∼y…

A: Revision : A relation ~ defined on a set  A is an equivalence relation if and only if it satisfies…

Q: 2. A relation p is defined on the set of all real numbers R by xpy if and only if |x-yl s y, for x,y…

A:

Q: Prove the understated statements concerning the relation &lt; on the set Z of all integers . If x…

A: To prove: If x&lt;y and y&lt;z then x&lt;z. Proof: The first inequality x&lt;y suggest that the…

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

Q: Let R be the relation on the set N0 of natural numbers given by the following rule: (n,m)∈R(n,m)∈R…

A: Let R be the relation on the set N0 of natural numbers given by n,m∈R if and only if n-m is a…

Q: Let X = R – (0,0) and - be defined over X by setting x-y - y = tx for some non-zero ! E R. (a)…

A:

Q: Find the number of different partions of a set (a) with one element (b) with two elements (c)…

A:

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: I. Determine whether each relation defined on the set of positive integers is reflexive, symmetric,…

A: Let R be a relation and (x,y)∈R if x=y2 , x,y∈Z+ (i) Reflexive : A relation R on a set A is said to…

Q: 2. A relation p is defined on the set of all real numbers R by xpy if and only if |x- yl < y, for x,…

A: