The relation by a = b (modn) is Partial Order Relation Ture O False O

Q: 1. Let H = {1, 2, 3, 4, 5} and the rlation RC H², with (a, b) ER + a = b( mod 3). • Give the set R.…

A: R ={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}

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: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

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Q: SULU Let R be a relation over the integers (Z). Prove that R= {(a,b) : a mod 4 = b mod 4} is an…

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Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: ntegers as: x Ry +x and y have the same remainder when divided by the integer a is an equivalence…

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Q: {(a, b) acb, a and b are finite set of integers}

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Q: . Define r on the power set of {1,2, 3} by ArB → |A| = |B|. Prove that r is an quivalence relation.…

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Q: 1. Express the following relations as a table and digraph. а. {(1,2), (1,3), (1,4), (2,1), (3,3),…

A: Relations as a table and digraph According to our guidelines,we can answer only first question.…

Q: 1) Let S be the equivalence relation on R defined by xSy iff x-y Q. Then a) [√3]-(-√3+r,req) b)…

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Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A| < [B|…

A: A partial order relation is total order relation if each of the pair of the elements are comparable.…

Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R?  Note: Select the order that…

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Q: Let A = { 2, 3, 4} and B = { 6, 8, 10 } and define a relation R from A to B as follows: For all…

A: Using relation property,

Q: The participation of relation R can be: total, partial, onto, and into. Given A = {1, 2, 3, 5} and B…

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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: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

Q: 3. Let S be the congruent modulo 2 relation on Z, that is m S n→2|(m-n). Show the relation S is: (a)…

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Q: 1.What is Relation?…

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Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…

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

A: This relation is Discrete.

Q: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

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Q: b( Let S be the relation defined on P ((1, 2, 3, 4}) defined by X SY if and only if IX| = |Y| (mod…

A: The complete solutions are given below

Q: Let the relation R defined on the set of positive integers as (x, y) ER if 3 divides X - y Determine…

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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…

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

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Q: Which relation has a domain of (3, 5, 8} ? O(2.8). (1. 3), (3, 5)} O(3, 8). (5. 3). (3, 5)} O (3.…

A: Domain of relation: The set containing all the first elements of all the ordered pairs of relation R…

Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Prove that the relation is an equivalence relation. 1. For x,y E R say x is congruent to y modulo Z…

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Q: Which of these relations on {0, 1, 2, 3} are equivalence ?relations

A: Equivalence relations are the relations which are reflexive (xRx), symmetric (xRy implies yRx),…

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: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A]< |B|…

A: Given T be the partial order relation on P1,2,...,20 defined by ATB if and only if A&lt;B or A=B.

Q: Let S be the congruent modulo 7 relation on Z, that is m Sn 7|(m-n). Show the relation S is: (a)…

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

A: Here we choose the correct option.

Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: As per answering guideline, we can answer only one question at a time. Please repost other question…

Q: Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R…

A: Introduction :Given , R : set of all binary relations on the set {1,2,3}We have asked to find the…

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: Draw the Hasse diagram for the following partial order. Domain: {3, 5, 6, 7, 10, 14, 20, 30, 60}. x…

A: Hasse Diagram : For a finite poset (P,⩽), the Hasse diagram is a graph with vertices x ∈ P such that…

Q: (a) How many functions are there from {1,2,3,4,5} to {A, B, C}? (b) How many onto functions are…

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Q: A relation R is defined on the set of all integers as xRy if x - 4y is greater than 5. Then the…

A: We have given that  , R is a relation defined on a set of all integers as x R y  if  x - 4y greater…

Q: Let A = {#, 7, x} and let R be the relation on A given by R = {(7, 7), (#, #)}

A: R is  said to be reflexive relation on A if for all x in A, xRx holds.  R is said to be symmetric…

Q: 6. (a) Let ~ be the relation on Mat2(R) defined by: A ~ B if and only if the (2, 1) entry of A – B"…

A: This problem can be solved as follows:

Q: Suppose there are two transitive relations R, S Disprove the claim that the composed relation S R…

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Q: Let be the relation on True False N defined by R={(n, m) : m³ = n + 1). Then R is one-to-one.

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Q: Suppose R is a relation defined on the set A = {1, 2, 3}. If R = {(1,1), (1, 2), (2, 1), (2, 2), (3,…

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Q: a L4 D 2 of 5 disprove that R is a partial order : {(a,b) : 3keza = k * b} be a relation over the…

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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…