Consider splitting a circle into n sectors. There are k >= 3 colors. We define an as the number of ways that this circle can be colored by k >= 3 colors such that no two consecutive sectors have the same color. Find a recursive relation for an for n >= 3.

Q: Use the "element chasing" method to show that: For all sets A and B, if B C A^C, then An B = Ø.

A: Here, we need to show that if x∈A, then x∉B provided B⊂Ac.  Or, if x∈B, then x∉A provided B⊂Ac.

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: X* +39

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Q: Lupe and Erik continue to argue about Chevrolet and Ford, and try to determine which is better. Lupe…

A: Given: Number of years = 15 years Value =$25,000. To find: Recursive rule for each Chevrolet and…

Q: The Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the…

A: Create the spreadsheet model that simulates the points scored by each team. Use at least 1,000…

Q: Fill in the missing element of B such that A = B. A = {7, 19, g, #, 2, 4, &, f, 17, 1, k} B = {#,…

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Q: Show that An, n > 5 is simple.

A: Sol:- To show that An, the alternating group of even permutations of degree n, is simple for n ≥ 5,…

Q: Which of the following sets are closed? Choose ALL that apply. Show the steps. I. The set of…

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Q: The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such…

A: Ans:- x= 35 I have done solution with diagram so that you can visualise this problem...and in this…

Q: uppose Var(X) = 93, Var(Y) = 98, and X and Y are independent. What is Var(.6X + .4Y)?

A: Answer: - Given,  Var(X) = 93, Var(Y) = 98, and X and Y are independent.                 What is…

Q: Let the letters G and B denote a girl birth and a boy birth, respectively. For a family of three…

A: Let the letters G and B denote a girl birth and a boy birth, respectively. Given that a family has…

Q: Show by contraposition that : Vx ERX2-3x - 1020 → x25 or x< - 2

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Q: Graph the set. [-4, 6] ⋂ [0, 8)

A: Given : The Set A = -4, 6 The Set B = [ 0, 8 ) We have to graph the set -4, 6∩[ 0, 8 )

Q: list all the subsets of  {1,2,∅}   and {{R}} R= real number

A: Number of subsets of a set with n elements is 2^n

Q: This

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Q: 1. Find the number of zeroes at the end of 100!

A: Introduction :Here, we have asked for the number of zeros at the end of 100 !

Q: Let A = {small, medium, large}, B = {yellow, magenta}, and C = {triangle, square}. List the elements…

A: The elements in A is {small, medium, large}.

Q: Differentiate 2xー4x -

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Q: . The relation ⋆ means “this number written out in English has this many letters”. For example, 6 ⋆…

A: A relation R  on a set A is said to (1) Reflexive : forall x in A implies (x,x) in R . (2)…

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: 12. {yly = x² - 1, x = integers}

A: {y/y=x2−1,x∈integer}

Q: I have to identify the recursive and explicit rule. I need to select two

A: Answer: Option F f(n)=f(n-1) . r Option A f(n)=3. 4n-1

Q: How many pairs of ordered numbers exist such that sum , product and quotient are the same?

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Q: The house of a row are numbered consecutively from 1 to 49 .show that there is a value of x such…

A:

Q: feois Pdf find

A: f(x) is the probability density function if the area under the curve is one and f(x)&gt;0

Q: Let A=[-1,7[,8={-1,3.10,12} and C={7}. Then (A-B) UC=

A: Given that A={-1,7} B={3,7,10,13} C={7}

Q: Consider the following sets: Express each set below using the roster method. Write all elements in…

A: AnswersB ∩ A = {3,5}(B ∩ A) - C = { }=ϕC - (B ∩ A) = {4,6,7}Explanation:(1)B intersection A means…

Q: The houses of a row are numbered consecutively from 1 to 49.show that there is a value of x such…

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Q: {(-5, 7), (-6, -8), (1, -2), (10, 3) }

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Q: Graph and write in interval notation the following: 8. (3,9) U[-2,8]

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Q: Compute r2

A: Given the calculated values, t value, t = 2.17

Q: Q = {E, A, A², A³, B, BA, BA², BA³} X,

A:

Q: If A= xe Z:2" = 1 and B = {x e Z:-4 < 3x-1<11}, then find n(A×B),where Z is a set of integers.

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Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…