Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b + 3} R3 = {(a,b) | a+b>4} a) Which of these relations are symmetric and why? If not symmetric give counter example. b) Which of these relations are reflexive and why? If not symmetric give counter example.

Q: - Recall that for x, y € R, x - y = R is the absolute value of x-y. That is, if x-y 20 if x-y<0. x-y…

A:

Q: The relation on the real numbers R defined by a ~ b if both a > b and b>a is not an equivalence…

A:

Q: Let A = {1,2,3,4} and B = {5, 6, 7}. Let f be the relation f = {(1,5). (2,5), (3,6), (?, ?)} where…

A:

Q: 3. The DIIOwing relations are not equi properties that are not satisfied. Explain your answer. a. a…

A:

Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: If 'I' denotes the 'divides' relation, then what can be said about 'b' if (2 | b) ^ (b | 2) (2…

A: there are two relations 2 is divisible by b and b is divisible by 2 and there is a disjunction(means…

Q: The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1,…

A: Infinite sets can also be grouped into equivalence classes, such that all the sets in a given…

Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is irrational OD…

A:

Q: 2 Explain why the relation on N defined as is not an equivalence relation. {(x,y): +y is a multiple…

A:

Q: Suppose the following relations are defined on the set of A = {-2, -1,0 1, 2, }, . List the pairs in…

A: For relation R on a set A.   R is reflexive if (a,a)∈ R, for every a∈ A.   R is symmetric if (a,b)∈…

Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

A:

Q: 9. The relation ~ defined on the set of natural numbers by a ~ b means 'a – b is even is : A. an…

A: Equivalence relation : A relation which is reflexive, symmetric and transitive is an equivalence…

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: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: Consider the following sets V = W = X = Y = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} {p EN:p is a prime…

A:

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

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

A:

Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

A:

Q: Plz explain properly.

A: The objective of this question is to find the Cartesian product of sets A and B, the relations R and…