A relation R is defined on the set, Z, of integers by xRy if and only if x+ y 2 5. R is A reflexive B symmetric C transitive D an equivalence relation 3.

Q: 4. Suppose R is a relation on a set A. The complementary relation R is defined by letting a R b if a…

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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 a relation on the set of all integers such that aRb if and only if a +b is even. Is R…

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Q: Let a relation ∼ on R2 = {(a, b): a, b ∈ R} be defined as: (a, b) ∼ (c, d) if and only if | a | + |…

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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 A × A , where A= {1,2,3,4} that is elements of this relation are pairs of…

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Q: Define the relation on the set Z of integers by if and only if a ~b if and only if a = b + 5k for…

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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: Define a relation " on Z by a ~ b if 3a + 4b = 7n for some integer n. Prove that - defines an…

A: A relation ~ on ℤ by a~b if 3a+4b=7n for some integer n.

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: 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: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

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Q: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

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Q: A particular relation * is defined on the set Z-{0} by x * y if and only if every prime factor of x…

A: Given that a particular relation is defined on the set ℤ-0 by…

Q: Q7. Let R be a relation on the set Z defined by the following rule: for all a, b e Z, a Rb if and…

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Q: 12. The relation R defined on the set of integers by a R b means 'a + b2 3' is A. Reflexive B.…

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: Define a relation on Z by a R b if a² = b². a. Prove that R is an equivalence relation. b. Describe…

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Q: on K³defined by: (a, b, c) {0} such that (a, b, c) = k(c, e, d) is an equivalence relation on K3,…

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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: 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: Show that the relation R on Z defined by aRb if and only if 5a−3b is even, for a, b ∈ Z, is an…

A: Let R be a relation from a set A to itself. R is said to be an equivalence relation if 1) R is…

Q: 3. Let A be the set of all subsets of the natural numbers and let RCA× A be the relation that (S, T)…

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Q: 2. Consider the relation on the natural numbers N defined as follows: for all x, y e N, xRy if and…

A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

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 the relation R on the set Z be given by the condition: (x, y) E Rif and only if x4 = y4. Answer…

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Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

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Q: ) Let S = {(x, y) E R × R: y – x is an integer} a) Prove the S is an equivalence relation on R b)…

A: Given, S=x,y∈R×R: y-x is an integer

Q: on K³defined by: (a, b, c) ~ (d, e, f) if and only if ak e K – {0} such that (a, b, c) = k(c, e, d)…

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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 X be the set of all subsets of ℤ . Define a relation R on X as follows: Given two subsets of…

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Q: Let R be a relation on Z defined by R = {(p, q) E Z × Z |p – q is a multiple of 3}. (a) Show that R…

A: Since you have asked a question having multiple subparts, we will solve the first three subparts for…

Q: A relation R on a set A is backwards transitive if, and only if, for every r, y, z E A, if rRy and…

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Q: 4|(x+3y)

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Q: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…

A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…

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: 2. Let H ≤ G and define = on G by a = b iff a¯¹b € H. Show that =µ is an equivalence relation.

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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 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: 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: Define a relation R on Z by declaring that xR y if and only if x^2 ≡ y^2 (mod 4). Prove that R is…

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Q: On P2, define a relation p(x) ~ q(x) if p(0) = q(0). (a) Show that this is an equivalence relation…

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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: 40

A: By using the definition of equivalence relation solution is given as follows :

Q: 1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x²…

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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 < 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.