12. The relation R defined on the set of integers by a R b means 'a + b2 3' is A. Reflexive B. symmetric C. antisymmetric D. transitive

Q: 5. Define a relation S from R to R as follows: For all (x,y) ERx R, (x,y) €S means that x > y. a. Is…

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Q: 9.32. A relation Ris defined on the set A = {a+bv2: a,b € Q, a + bv/2 + 0} by x R y if æ/y E Q. Show…

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Q: let A={1,2} and B={1,2,3} and define a relation R from A to B as follows: given any (x,y)E AxB…

A: Given: A=1,2 and B=1,2,3 and R:A→B such that x,y∈R⇒x-y2 is an integer. To find: A×B  and R…

Q: Let A = { 2, 3, 4 } and B = { 6, 8, 10, 12 } and define a relation R from A to B as follows: %3D For…

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Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

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Q: 2. Define the sets X = {1,2,3} and Y = {4,5,6}. Now, define the relation R from X to Y by „R, if and…

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Q: 1. Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible…

A: According to question given that Set Z in which the relation R is defined by aRbIf and only if a+3b…

Q: Prove the understated statements concerning the relation < on the set Z of all integers . If    x…

A: x = y  and     O < z

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: Assume R is a relation Dver set A. a) prove Ris anti-ceflective 1 Diaw graph G(LE) where the…

A: A relation R on a set X is said to be anti-reflective if no element  of X is related  to itself…

Q: Let A = { 2, 3, 4, 6 } and B = { 6, 8, 10 } and define a relation R from A to B as follows: For all…

A: Given that : A = {2, 3, 4,6} and B = {6,8,10} define relation  A*B→R R = {(x ,y): yx is an integer ,…

Q: Given a relation from Z (positive integer) to Z (positive integer) is defined as follows: ((m, n) E…

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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 irrational OD…

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Q: 9.19. A relation Ris defined on Z by x Ry if x · y > 0. Prove disprove the following: (a) R is…

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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: Show that given relation is Symmetric For X, y e R say x is congruent to y modulo Z if x - y is an…

A: This question is related to number theory.

Q: 1. Let Y = (0, 1, 2) and Z = (0, 1) and define as relation R from A to B as follows: Given any (x,…

A: (NOTE- The relation R should be from Y to Z instead of A to B.) Given sets are, Y=0,1,2 and Z=0,1…

Q: A relation R is defined on the set of integers by: aRb = a + b = 2m + 1, where m is an integer. Show…

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Q: 1. Prove that “divides" is a transitive relation. That is, prove that, for all integers a, b, c, if…

A: I the given question we have to prove that , for all integers a,b,c, if a|b and b|c, then a|c.

Q: 1) Let S be the equivalence relation on R defined by xSy iff x-y Q. Then a) [√3]-(-√3+r,req) b)…

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Q: 1. Let & be the relation of (a,b) la #b] on the set of integers. What is the reflexive closure of R?

A: As per our company guideline we are supposed to answer only one question with its 3 subparts. Here…

Q: 4. Suppose Rand S are symmetric relations on a set A. Prove that RoS is symmetric iff Ro S = So R.…

A: Suppose R∘S is symmetric Let s, r∈S∘R ⇔r, s∈R∘S⇔s, r∈R∘S ( since R∘S is symmetric)  So, R∘S=S∘R

Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

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Q: 4.4.5 Write out the following relations as subsets of the Cartesian pod (a) The relation on N…

A: (a) The relation given is already a subset of the Cartesian product N x N. It can be written as…

Q: Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

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Q: Let A = {2, 3, 4} and B= {6, 8, 10} and define a relation R from A to B as follows: For all (x, y) ϵ…

A: Relation: A set is a ordered pair  is defined as a relation Let us consider the set A and B , then…

Q: 1 If MR =: 1 lo 1 1., then the relation ol 1 Ris Reflexive Transitive Anti-symmetric Symmetric

A: To find: The type of relation R. Concept used: Reflexive: If all the diagonal element of MR is 1,…

Q: 14. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A →B as follows: For all…

A: Given sets  A={9,11,12,14} and  B={1,2,3,4}  The relation R from A to B is defined by ,…

Q: 9. (i) Prove by mathematical induction that for n e N, Ar? – 1 2n + 1 (ii) A relation R, is defined…

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Q: Let S be the set of integers. If a, b E S, define aRb if ab >= 0. Is R anequivalence relation on…

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Q: 5. Let A = {1, 2} and B x+y y) e R such that {3,4}and define a relation from A to B as (x,y) e AxB…

A: We will find out the required values.

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: Define a relation S from R to R as follows:…

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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: 1. Determine whether the relation R on set Z (set of integer number) is reflexive, irreflexive,…

A: We determine whether the relation R on the set Z is reflexive, irreflexive, symmetric, antisymmetric…

Q: Let A = {4, 5, 6} and B = {5, 6, 7} and define relations R, S, and T from A to B as follows: For all…

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Q: et A={1,2} and B={1,2,3} and define a relation R from A to B as follows: •Given any (x,y) element A…

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Q: Let D = {2,4,6} and E = (1,3,5}, define a relation R from D to E as follows, given that…

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Q: Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} issymmetric but neither…

A: Given, relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)}.

Q: Let R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

A: Given R is a relation from set A to B. Let R is symmetric relation and R-1 be the inverse relation…

Q: The relation xy >= 1 where x,y are on the set of all integers is reflexive. True False

A: Given relation xy≥1, where x,y are on the set of all integers

Q: A relationR is called a partially ordered set if R is: .a reflexive .b antisymmetric .C transitive…

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Q: Our universe U is Z (integers), and R is the relation defined by R(x,y):=x<y^2 For example,  R(3,-2)…

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Q: 7.1.6 For the relation R = {(x, y) : x < y} defined on N, what is R-1, and what is the intersection…

A: The detailed solution is as follows below:

Q: Let A = { 2, 3, 4 } and B = { 4, 6, 8, 10 } and define a relation R from A to B as follows: %3D For…

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Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below

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: 6. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A →B as follows: For all…

A: Answer for sub question a: Given A=9,11,12,14, B=1,2,3,4. The relation R:A→B is defined as follows:…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.