Given a relation R on Z defined by mRn 3|(m – n) for all m, n E Z. Find the equivalent class determined by 4.

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A: Equivalence relation

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Q: whence (R3 o R2) o R1 = R3 0 (R2 o R1).) %3D Using the result above, show using induction that, if R…

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Q: relation R on Z defined

A: Given, a relation R on Z defined by mRn ⇔ 7|(m − n) for all m, n ∈ Z.

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

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A: This question is related to number theory.

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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: 10. (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: Given a relation R on Z defined by mRn ⇔ 3|(m −n) for all m, n ∈ Z. Find the equivalent class…

A: We have the relation defined by mRn⇔3/m-n Now ,we need to find the equivalence class determined by…

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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 K be an extension of be an algebric element o 2 F Show that a ² is algebr

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Q: Q1 Given a relation R on Z defined by mRn7|(mn) for all m, n € Z. Find the equivalent class…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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Q: Let H(x):=k for x=, (keN) and H(x):=0 elsewhere on [0,1] Show that H(x) 4ER[0,1].

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Q: 6. Is the function h: Z → Z defined by ( 2n if n 20 h(n) -n if n < 0 one-to-one? Is it onto?

A: The solution is given as follows

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Q: . Let X be a r.V. such that E(X") is finite for all n = 1, 2,... Use the expansion

A: Introduction: Suppose X is a random variable. Then, the moment generating function (mgf) of X is…

Q: 2. Using the result above, show using induction that, if R is a relation on A, then R" o R = Ro R"…

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Q: If m, n are relatively prime, then o(mn) = o(m)o(n)

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Q: Suppose that f: C C is a holomorphic function such that there is a fixed kEN for which =1, for all.n…

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Q: Let o,T E Sn for some positive integer n satisfy o(k) 1< k < n. Prove that o-(k) = k and p(k) = k…

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Q: Let a > 1 be an integer. Prove that n|p(a" – 1), where o is the Euler ç-function.

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Q: Let A ∈ Mn×n(F). Under what conditions is det(−A) = det(A)?

A: In determinant the scalar quantity is taken common from a single row or a column.

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Q: 2. Write a preference E on R as a subset of R', where a bundle a E Rª is at least as good as a…

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Q: 2. Using the result above, show using induction that, if R is a relation on A, then R" o R= Ro R"…

A: In this problem, we have to show that if R is a relation on A, Rn ∘ R = R ∘ Rn, for each n ∈ ℕ. We…

Q: Let E be the set of all positive even integers. Prove that E is countably infinite by defining a map…

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Q: Prove that for any k > 0, nk e o(2v™).

A: The complete solutions are given below

Q: Prove that det(kA) = kn det(A) for any A ∈ Mn×n(F).

A: In determinant the scalar quantity is taken common from a single row or a column.