A relation R is defined on the set of integers by: aRb = a + b = 2m + 1, where m is an integer. Show that R is not an equivalence rélation.

Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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Q: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

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Q: Let R be a relation on the set of all integers such that aRb if and only if 3a – 5b is ever 1) Is R…

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Q: Consider the relation K on N defined by Knm iff n <m.Which statement below is true? K is an…

A: It is Irreflexive.

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: Let Z be the set of integers. Consider R = {(x, y) e Z × Z: 7 divides x-y}C Z × Z. Show that R is an…

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Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: consider the relation ∼R on P(N), the power set of N, with A  ∼R B iff A∩B ≠ ∅ determine whether…

A: consider the relation ∼R on P(N), the power set of N, with A  ∼R B iff A∩B ≠ ∅

Q: A relation R is defined on the set of real numbers by xRy if and only if x-y is a multiple of 3.…

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Q: Let R be the relation on the set of ordered pairs of positive integers such that  ((?, ?), (?, ?)) ∈…

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Q: Define the relation ~ on the set Z of integers by m~n if and only if m^2 = n. Show that ~ is not…

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Q: Let S be the set of real numbers. If a, b e S, define a - b if a – b is an integer. Show that ~ is…

A: Definition of the equivalence relation helps to prove the required. A relation is said to be an…

Q: Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b} is an…

A: Given, the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b}.

Q: efine the relation ~ on the set N of positive integers by a~b if and only if  a = b(10^k) for some…

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Q: Let R be the relation on the all integers given by xRy iff x- y 2k for some integer k. (1) Prove…

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Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x –…

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈…

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Q: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

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Q: Subject: Set Theory

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Q: Given the relation R- {(1,1), (2.2). (3,3).(4.4), (1,2). (2,1). (3,4), (4,3)) on the set X…

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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: Show that the relation R defined on the set of integers ℤ by (a,b) Î R if a – b = 6k for some k Î ℤ…

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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Q: Define a relation on the set {a, b, c, d} that is 6. (a) irreflexive and transitive, but not…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: A relation R is defined on Z by a R b if |a – b| < 2. Which of the properties reflexive, symmetric…

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Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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

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Q: 9.15. A relation R is defined on Z by a Rbif |a – b| < 2. Which of the properties reflexive,…

A: Given : A relation is R is defined on Z is given by  a R b if a-b≤2  Which of the properties…

Q: let R be an equivalence relation and let [x] be the equivalence class of x, prove x belong to [x]

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Q: Let R be relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) e R…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: . Define a relation on R²\{(0,0)} by letting (x₁, y₁)~(x₂,Y₂) if there exists a nonzero real number…

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Q: Let us consider the following relation R on the set of all pairs of integers: (a,b)R(c,d) if a = c…

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Q: Use a particular counterexample to explain why R fails to be an equivalence relation is the…

A: We take counter example   9R10,10R11⇒9R  11

Q: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

A: Given a relation, aRb⇔ab≤0. To check whether R is an equivalence relation on set ℤ. A relation is an…

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 =…

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Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: Then R is (a,x)R(b, y) if…

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Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: For universe S = R², define relation ~= as: (a,b) ~= (c,d) < 2a - b = 2c - d Prove that ~= is an…

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Q: On the set {(a, b)} of all ordered pairs of positive integers, define (x1, Y1) ~ (x2, Y2) if and…

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Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the…

A: Let S be a nonempty set. Consider the relation ~ on P(S)  defined by A~B if A∪Bc=S To show: "~" is…

Q: Show that the relation R defined on the set of integers ℤ by (a,b) ∈ R if a – b = 6k for some k ∈ ℤ…

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Q: Prove that the given relation is an equivalence relation, and describe the distinct equivalence…

A: Let A is the set of all students at your college. For every x,y∈A,  xSy⇔x is the same age as y. That…

Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ER…

A: A ={ (a,b) : where a and b are positive integers}  R= {(a,b) and (c,d) : a+d= b+c }  We have to…

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.