A relation R is defined on the set of real numbers by xRy if and only if x-y is a multiple of 3. Show that R is transitive.

Q: be an integral domain and define a relation - on DXD such that b+0 and dz0 by (a,b) - (c, d) if and…

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Q: 35. For each real number x, let f(x)=x². For any two real numbers a and b, define a -b provided that…

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Q: i Determine whether or not the relation R on the set of all real numbers is reflexive, symmetric,…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: f) Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric? g) Is…

A: Use the definition of antisymmetric to check whether the given relation is antisymmetric or not.…

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: Show that the function g: R - R defined by g(x) = 4x² + 3 is neither one-to-one nor onto

A: To show the function g:R→R defined by gx=4x2+3 is neither one to one nor onto. Solution: First we…

Q: Show that if ƒ is both even and odd, then ƒ(x) = 0 for every x in the domain of ƒ

A: Given, function f is both even and odd function.

Q: Given an arbitrary relation R, suppose we compute two new relations: • R1, the reflexive closure of…

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Q: Suppose both f(z) and the conjugate of f(z) are holomorphic on a connected open set.  Show that f is…

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Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

Q: Define a relation D on the set of real of numbers as follows: Vx, y ER, xD y ⇒x-y is rational…

A: Correct option is  D is reflexive , symmetric and transitive.

Q: Define a relation D on the set of real of numbers as follows: Vx, y ER, x Dy ⇒ x-y is rational…

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Q: a. Prove that Rf is an equivalence relation. b. Suppose that f is the squaring function defined by…

A: This is a problem of Relation.

Q: Show that the function g: R -R defined by g(x) = 4x2 +3 is neither one-to-one nor onto

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Q: Show that the relation R defined in the set A of all polygons as R = {(P1, P2) :P1 and P2 have same…

A: Given, relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same number…

Q: Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric?

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Q: Let the relation non z defined by x ny if and only if 3/(x+2y) Show that n is an equivalence…

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Q: A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the…

A: Relation: Let A  and B  be two sets then relation between A nd B means  the collection of the…

Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

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

A: Consider the relation  for  Reflexive: For   Thus,  is not reflexive. Symmetric: For  but…

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

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Q: Let f(z) be an ODD fanetion. If the point (2,3) belongu to f, then another point likely to (0,0) (2,…

A: Given f(x) is odd function.

Q: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b) : |a –…

A: Given: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b)…

Q: T is a function?

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Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b}.…

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Q: A relation R defined on the given set A will satisfy

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Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

Q: Let p be an integral domain and define a relation - on DxD such that bz0 and dz0 by (a,b) -~(c,d) if…

A: R is the symbol for relation.     Symmetric:    if (a,b)R(c,d) ∈ D×D   ⇒ad=bc   ⇒bc=ad   ⇒(c,d) R…

Q: A relation R defined on the set of real numbers is such that x R yand y Rx >x = y. R is said to be…

A: Properties  used :- (i) a R a  for all a∈ A, [Reflexivity] (ii) a R b  and  b R a ⇒ a = b,…

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

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Q: Show that if for a relation R we know that R2 C R, then R transitive, and conversely. Ent. There are…

A: To prove whether a relation is transitive or not

Q: A relation R, is defined on Z, the set of integers by aRb + a - b is even. Show that R is…

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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: Let R be the relation on the set of real numbers such that x R y if and only if x and y are real…

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

A: Definitions of symmetric, reflexive,transitive are given.We have to check them .

Q: Determine whether the relation R on the set of integers is reflexive, symmetric, antisymmetric,…

A: We have to determine whether the relation R on the set of integers is reflexive, symmetric,…

Q: Let T be the relation in the set of real numbers IR defined by xTy of both xe [n, n+1] and ye[nin+1]…

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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: A relation * is defined on the set R-{0} by x * y if and only if xy > 0. For each of the following…

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Q: Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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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…

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

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Q: Show that the relation R in the set R of real numbers, defined asR = {(a, b) : a ≤ b2} is neither…

A: Given,  relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2}.

Q: i Determine whether or not the relation R on the set of all real numbers is reflexiv netric,…

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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…

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,…

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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.