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

A:

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 = {#,…

A:

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

A:

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: 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

A:

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 -

A:

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…

A:

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: feois Pdf find

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

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

A:

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

A:

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: 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…