A. Convert the binary number 111010101.110111 to hexadecimal. B. Determine the power set of the set A={q,p,x}. C. Let the relation R be {(1,2), (2,9), (5,6)}. Is R transitive? Give the reason.

Q: Consider  the relation R={(a, b),(a, c),(c, b),(b, c)} on  the set A={a, b, c}. Is R reflexive? Is R…

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Q: Define a binary relation P on Z as follows: For all m, n ∈ Z, mP n ⇔ m|n . (i). Is 5P25? Is 2P27? Is…

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Q: Define a relation R on Z as follows: For all integers m and n,   m R n ⇔ 5 | (m2 − n2).   Is 1 R…

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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: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is…

A: Given, relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}.

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: Let S be the set of real numbers. If a, b e S, define a - b if a – b is an integer. Show that ~ is…

A: Definition of the equivalence relation helps to prove the required. A relation is said to be an…

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: 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: 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: 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: let R be the relation on the set of positive integers in which a R b if and only if a is a factor of…

A: Given below the detailed Solution.

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: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀a, b∈N:…

A: This is a problem of relation.

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

Q: b) E Rif and only if a has the same first name as b. (Check all that apply.) Check All That Apply…

A: We need to check whether the given relation is reflexive, symmetric, transitive, antisymmetric. here…

Q: Subject: Set Theory

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Q: Which ONE of the following represents an equivalence relation on the set of integers? Vx.y€Z, xRy if…

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Q: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N…

A: (a) let (a,a) be in Rc .      Then there exist integers u and v such that       au + av = c…

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

A: Given :-

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

A: We will find whether the relation is reflexive, symmetric or transitive as following.

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: 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: Determine whether or not the relation ? on the set of all people is reflexive, symmetric,…

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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 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 N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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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 R be the relation on the set of integers Z defined by m Rn iff m +n = 16. Determine whether R is…

A: Here, relation defined is, mRn iff m+n=16

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 us consider the following relation R on the set of all pairs of integers: (a,b)R(c,d) if a = c…

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Q: Determine whether the following relations on the set of integers are reflexive , symmetric,…

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Q: Consider the relation on Z × Z given by aRb if a &lt; b. Is R transitive. Answer yes or no…

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Q: Select the following relations on Z that are equivalence relations. ○{(a,b) ||a| = |b|} {(a,b) a²b²…

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Q: t R be the relation on the set of ordered pairs of positive integers ch that ((a,b), (c,d)) e R if…

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Q: (a) Determine whether the relation ~ on C with 2₁ ~ 22 iff z1 = 22 is reflexive, whether it is…

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Q: Consider the set Q = Z ×(Z 10), and the relation tupon QDefined as: (a, b) ↑ (c, d) e a·d=b·c a - d…

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Q: etermine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not…

A: Denote R by the relation on the set S={a, b, c, d} that is irreflexive, symmetric and not…

Q: 5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence…

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Q: Determine which of the folowing relations R on Z are oquivaknee relatinns. If R is not an equivakner…

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Q: Determine whether the relation ? on the set of all people is reflexive, symmetric,  antisymmetric,…

A: We have to determine whether the relation R on the set defined in the parts (a) and (b), are…

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: Let ∼ be the relation on Mat2(R) defined by: A ∼ B if and only if the (2, 1) entry of A − BT equals…

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Q: 8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d)…

A: Equivalence relation