b( Let S be the relation defined on P ((1, 2, 3, 4}) defined by X SY if and only if IX| = |Y| (mod 2). Write down the full nature and characteristics of relation S (similar to what is asked in Part a).

Q: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: 0,1,2

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Q: A relation Ris defined on N by a R b if a/b e N. For c, d e N, under what conditions is c R1 d?

A: An inverse relation is the set of ordered pairs obtained by interchanging the first and second…

Q: 1. (p.209, #16) Define a relation R on Z by declaring that xRy if and only if x? = y? (mod 4). Prove…

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Q: Fuppose that the relation R indicates whether c articular student is registered for a particular c…

A: In this question, the concept of Relation is applied. Relation The relation is a relationship…

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: Let A={5,6,7,8,9,10} and define a relation S on A as follows xSy 2|(x-y) (a) Is 5S6? Why?

A: Consider the provided question,

Q: The relation R on the set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is defined by R= {(x, y) E AXA: x…

A: Here according to the definition,       R = {(x,y) : x = y mod 3} Then if y = 7, then x must be 7…

Q: Let A = {x, y} and let S be the set of all strings over A. Define a relation C from S to S as…

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Q: Let A be the set of all strings of 0's, l's, and 2's of length 4. Define a relation R on A as…

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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: C. Let T be defined onN N by (a, b)T (c, d) if and only if a c and b 2 d. Write down the full nature…

A: We will use the basic definition of reflexive, symmetric, antisymmetric and transitive realtion.

Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

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: 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: 3. Let R be the relation defined on P({1,..., 100}) by ARB if and only if |AU B| is even. Is R…

A:

Q: Which of the following is/are true for the relation R, where a is related to b (aRb), if and only if…

A: Suppose, A be any set and suppose R:A->A is a relation. Then, R is reflexive: if for every x in…

Q: 1. Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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Q: T is a function?

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Q: Let R1 be the relation on Z+ such that ¤R¡y if and only if ry > 3. (Recall that Z+ = {1,2, 3, 4,…

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

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Q: a. Define a relation R on Z as follows: For all integers m and n, mRn + 3|(m – n). Then 3R5 (A) True…

A: We have to check whether given statement is true or false.

Q: y)∈R means that x²-y² is a nonnegative integer. Which of the following is true?     a. 1 R 2 b. 2 R…

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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 A x…

A: Given

Q: 10. (1) A is the relation defined on Z as follows: for all x, y = Z, x Ay ⇒x=y (mod 3). Describe the…

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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. For each of the following relations, indicate whether the relation is reflexive, anti-reflexive,…

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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: Let G = {-2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows. For every (x,…

A: Given,            G=-2, 0, 2  and   H=4, 6, 8and  define a relation v from G to H as follows.For…

Q: Let R be a relation defined on Z as follows: (a,b) is an element of R if and only if the square of a…

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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: 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: Prove or disprove the relation C on Z defined by C = {(x, y): x=y (mod 5)} satisfies the two…

A: I just used the definition of congruence and divisibility

Q: 4. Let G = {–2, 0, 2} and H = {4,6, 8} and define a relation V from G to H as follows: For all (x,…

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Q: 2. There is a function f : X →Y . Let's define a relation R in a set X, by a formula: (xRy) → (f(x)…

A: Given f: X → Y and R is the relation in the set X such that x R y ⇔ f(x) = f(y)

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 S be the congruent modulo 7 relation on Z, that is m Sn 7|(m-n). Show the relation S is: (a)…

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Q: Which of the following definitions for the relation R (defined below) on A would constitute an…

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Q: Define the following relations on A = {0, 1,2,4}. Answer each of the following questions by listing…

A: I am going to solve the given problem by using some simple algebra to get the required result of the…

Q: 2. Define a relation C from IR to IR as follows: For any (x, y) E IR x IR (x, y) EC means that x2 +…

A: We will use basic definitions of relation.

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: 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: Define a relation R from R to R as follows: For all (x, y) ER×R, (x, y) eR if, and only if, x = y? +…

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Q: In this exercise, you want to show that a relation RC A? is transitive + R"C R for all n E N = {1,2,…

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Q: 1. For this question, use N as the universal set. Define f = {(X,Y) E P(N) × P(N) : XUY = N and XnY…

A: Given that N(set of Natural numbers) is a Universal set. Also, given is a relation from P(N) to…

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: Which of the following statements is TRUE? sgn( (5 8) )=1 Let R be a relation on Z defined by xRy if…

A: ?Relation R is not Reflexive, because 2+2=4 does not divisible by 5. So , (2,2) not in R. ?…

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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