For the following relations on the set of POSITIVE integers, determine if it satisfies each of the following conditions: m~ n 19 divides m - n m~n 13 divides m + n 13 divides mn m~ n Reflexive Please enter Y or N in each of the boxes. Symmetric Transitive Equivalence Relation

Q: Define two relations R1 and R2 on set positive integers. R, = {(a,b)|a > b} and R2= {(a,b)|a? = b }.…

A: Composition of relation

Q: 4 1) 3 bes this digraph illustrate a relation that is symmetric or transitive or neither? ymmetrid…

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Q: for the following relations on 2 the set A = {1, 2, 3}: R = {(1, 1), (1, 2), (1, 3), (3, 3)},…

A: A relation R is an equivalence relation if it is: i) Reflexive: if aRa for all a in A ii) Symmetric:…

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and…

Q: If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence…

A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

Q: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a =…

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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: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

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Q: Give an example of relation on {1,2,3,4} that is reflexive, not symmetric, and not transitive

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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: (d) Justifying your answer, find the smallest set of related pairs which must be added to R in order…

A: We know that a relation is called an equivalence relation if it is reflexive, symmetric and…

Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

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Q: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

A: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

Q: Let IR be the set of real numbers, A = {r e IR: 5<x< 10}, B = {x e R: 73x<20}, C = (0, 10], D = (9,…

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Q: Let R be the relation, {(a, b) Nx N: a + b² is divisible by 3} Give an example that shows that R is…

A: Symmetric Relation: A relation R is said to be symmetric if

Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; Az : %3D %3D %3D {2,4,…

A: Let A=1,2,3,4,5,6 and 3 subsets of A. A1=1,3,5; A2=2,4,6,A3=3,6 we have a relation xRy if and only…

Q: The number of relations on the set A = {1, 2} is 256 . O True False

A: Number of relation with n elements 2n2

Q: Give examples: For each of the four relations between natural numbers x and y in the left column of…

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Q: For the relations: A x B, such that: A = {37, 38, ..., 42} and B = {42, 43, ..., 47} Count how many…

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Q: What is the possible number of reflexive relations on a set of 5 elements?

A: Introduction : We have give a set of 5 elements , we have asked for the number of reflexive…

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: Step 1:   The given relation is defined as: