Show that if E has finite i

Q: prove th na

A: The equation given is ,  ∇×F¯θ=1rsinθ∂Fr∂ϕ-1r∂r·Fϕ∂r. The curl of the function is given as, curl…

Q: Suppose a E Z. Prove that if a³ 1 (mod 5), then a # 1 (mod 5).

A: In this question, we use the method of contradiction to prove the desired result.

Q: What does the K stand for in Kn? (Finite)

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Q: in lim (1- = e Select one: O True False

A:

Q: Is given in th

A: The most repeating games used by the researchers that can be played quickly. It is discovered that…

Q: Assume an unlimited supply of coins worth 5 cents and 9 cents. Prove that some

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Q: Show that im n /-

A: Limit of the sequence

Q: . Prove the following: If gcd(a, b) = 1 and ca then gcd(b, c) = 1

A: We will prove the given statement.

Q: Prove Simple disprove is Bing That Characteristic af Prime or either Zero or

A: A simple ring R is a ring with unit such that the only two-sided ideals are R and (0). The…

Q: Show that 100 1 arctan(100) – arctan(2) + Σ 1 < arctan(100) – arctan(2) + 1+ 22 1+ 1002 1+ k2 k=2 WI

A: Note that the function f(x)=11+x2 is a monotone decreasing function, i.e., f(x1)&gt;f(x2) whenever…

Q: Find aly if and of to

A: Differentiation

Q: In Euler phi Function (n) # |U(n)||

A:

Q: Show that for any Positive integers iandj with

A: For proving this we take the Chebyschev  polynomial of second kind, So we have Tmx=cosmx for m≥1 Now…

Q: Prove bey wnduc hiou that for n22.

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Q: let by a fi

A:

Q: Let Σ be a set of well formed formulas and α, β be well formed formulas. Show thatΣ ∪ {α} |= β if…

A: If Σ⊨(α→β), and (Σ∪{α}) holds, then both Σ and α hold (a set is only true if every member of the set…

Q: 8. Suppose E is a nonempty subset of R. Show E = aEUint(E) %3D

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Q: Prove that the order of a k-cycle in S, is k.

A: Suppose σ is a k-cycle in the group Sn. then we follow that σ is a permutation of length k in which…

Q: 1 ient of in al</z] <2 is

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Q: What is the Increasing,Decreasing, and Constant Therom

A: Definition of increasing, decreasing and constant theorem

Q: Theorem 24. If ɛ > 0, then there is an integer N EN such that 0 < + < e. .

A:

Q: If ø (n) is Euler's Phi function then ø (22) = 8

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Q: Prove by Contradiction that if    a 0, which implies  a< = b

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Q: Prove that xk = x* mod |G| for x € G for any integer k.

A: Prove it considering two cases.

Q: п(п + 1) Show that , k 2 k=1

A:

Q: From

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Q: Prove that Fisher's ideal index number lies between Laspeyre's and Paasche's index number

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Q: Prove that √ ²07²dx = √= So e

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Q: Find the Maclaurin serie: e2x

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Q: Let a that Note: 1 6- a

A: we have been given that the function f is a continuous function. So, first, we will define the…

Q: Suppose x is a fixed real number with x 2 -1. For n2 1, prove using mathematical induction: (1+ x)"…

A: Here we will show that given statement is true by mathematical induction method.

Q: 4. Show that if ð > 2, then G contains a cycle.

A: We need to prove that δ≥2 , then G contains a cycle , Asume that G is a finite graph, Let V1 ∈ G,…

Q: Let T = > Σ - In k. n n=1

A: We will solve here only (a) part of 2.   we have to show that the sequence Tk is monotone…

Q: Find integers x and y such that gcd(N, 11353) = Nx + 11353y.  Let N = 116023

A: The greatest common divisor(gcd) of a prime number and any other number is always equal to 1.

Q: 3. Prove that eª >1+x for x > -1

A:

Q: 1. Use Euler's Theorem to prove a = a (mod 105) for all a E Z.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: let pcoc) =e" Since). oc G C-},3)

A: The given function is Fx=exsinx, where x∈-π2,π2.  If f'(x)&gt;0 at each point in an interval I, then…

Q: Let sk En(0.1)" n=1 Find s9.

A: Given that sk=∑ n=1k n (0.1)n -(i) Our Aim is to find s9=?

Q: In Euler phi Function Ø(n) |U(n)|

A: False  because correct statement  ϕ(n)=|U(n)|

Q: Let φdenote the Euler phi-function. Answer a and b (a) If n = 2a3b, for natural numbers a, b, show…

A:

Q: Find A- if A

A: This question is taken from the system of equations in which we have to find the inverse of the…

Q: Suppose that every student in a discrete mathematics class of 25 students is a freshman, a…

A:

Q: Prove that if x ~ Exp(X), then E (x) = .

A: Thank you for posting the question. Since you have asked multiple question, we will solve the first…

Q: let A to have0 al an must by

A:

Q: Is there any n n for which U2n = Dn?

A:

Q: if N=xYフ。 Prove tha+ xx

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Q: 2. Show directly that sup(4) = 1 for A = {1- : n eN}.

A: As we know that, 1&gt;1-1n ∀ n∈ℕ Therefore 1 is the upper bound of the set 1-1n:n∈ℕ. And for each…