1. The addition on P is commutative. 2. The multiplication on P is associative. 3. The relation < on P is transitive.

Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

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Q: Prove that for any set relation R (we did not pick it to be "on" any particular set) R* =N{Q:RC Q^ Q…

A: Given that any set relation R.

Q: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17}…

A: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17} For…

Q: Define a relation  P on Z as follows:  For all m,n∈Z,  mPn⟺m and n have a common prime factor. Is…

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Q: B if there exists o E Sn so that oao- = B. Prove that For a, B E Sn, let a ~ equivalence relation…

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Q: PROBLEM1 Instruction: Prove that the relation is  an equivalence relation.  For x, y ∈ R say x is…

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Q: ntegers as: x Ry +x and y have the same remainder when divided by the integer a is an equivalence…

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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: 13) Let A = {2, 3, 4, 5, 6, 7, 8} and define a relation R on A as follows: for all x, y € A, хRy+3|…

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Q: Define a relation P on Z as follows: For every ordered pair (m, n) E Z × Z, m P n + m and n have a…

A: a. 15 P 25 [Yes]Explanation:15 = 3 × 5 and 25 = 5 × 55 is prime so both of these numbers have a…

Q: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P

A: Concept:

Q: 11. Prove or disprove: if a relation R is transitive, then R-1 is transitive.

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Q: for the following relations on 2 the set A = {1, 2, 3}: R = {(1, 1), (1, 2), (1, 3), (3, 3)},…

A: A relation R is an equivalence relation if it is: i) Reflexive: if aRa for all a in A ii) Symmetric:…

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

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: 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: The participation of relation R can be: total, partial, onto, and into. Given A = {1, 2, 3, 5} and B…

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Q: (d)Give the equivalence class of string s = '1010' with respect to the relation R [*1010') =

A: .

Q: Consider the following relation on {1,2,3,4}. Check is equivalence or not? R= {(1, 1), (1, 2), (2,…

A: Follow next step

Q: Suppose A is a set having n elements. a. How many relations are there on 4? b. How many reflexive…

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Q: In each item below, verify that ~ is an equivalence relation on the given set. (a) Let S = Z x N.…

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Q: 3. Let S be the congruent modulo 2 relation on Z, that is m S n→2|(m-n). Show the relation S is: (a)…

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Q: Both P and Q are transitive relations on set X. Proof that a. Pn Q is also transitive b. PoQ is also…

A: Given,    Both P and Q are transitive relation on set X.

Q: 11 Let S be the congruent modulo 5 relation on Z , that is m S n → 5|(m – n) . Show the relation S…

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Q: Suppose that P is a unary relation symbol, Q is a binary relation symbol, f is a unary function…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: 2. Draw a Hasse diagram for the POSET(S,R) where S = {1,2,6,8,12,18,48,72,108,144,216,432} and R be…

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Q: The order of the reccurrence relation C+2 =-42 Ck22 is k-1 %3D k+2 ОА. 4 ОВ. 2 O C. 1 None of them O…

A: Order of the difference equation is the difference between the highest and lower subscript of…

Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: Equivalence relation

Q: Show that given relation is transitive For X, y € R say x is congruent to y modulo Z if x – y is an…

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

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Q: Proving a divisibility relation is transitive

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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: 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: O Let X = {1, 2, 3, 4, 5}. How many relations are there on X with the property that for all x E X, x…

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

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: 3. Let S be the congruent modulo 2 relation on Z,that is m S n→ 2|(m-n) . Show the relation

A: A relation is called symmetric if for any  if  then we have .

Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

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Q: Given the relation R on the set of all integers defined by the rule (x, y) ER if and only if x 2 y².…

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Q: Consider the equivalence relation E on N defined by Enm iff n-m is divisible by 4. Which statement…

A: An equivalence relation E is defined on the set of natural numbers N as  Enm denotes that n is…

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

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Q: 2. Consider the following relations on the set of integers: R1 = {(a, b) | a b}, R3 = {(a, b) | a =…

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Q: 3. Suppose that we have the following four tuples in a relation S with three attributes ABC:…

A: Given: Let us consider the four tuples, ABC:1,2,3,4,2,3,5,3,3,5,3,4. Let's determine the…

Q: 1. Let A = {1, 2, 3, 4, 5, 6}. Write out the relation R that expresses | (divides) on A.

A: The relation R that express |(divides) on A is represented by, R={(x,y)| x,yϵA, x|y}

Q: 7b, 7c, and 7d

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Q: Let be the relation on True False N defined by R={(n, m) : m³ = n + 1). Then R is one-to-one.

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Q: ave a class boundary that is less than zero?  On the probelem I am working, the class goes from 0-5

A: Class boundaries are the values which help in separating the data points in statistics.

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…