A student claims that he does not need to define permuta- tions because he knows the Fundamental Counting Princi- ple. What do you say?

Q: 2. A derangement is a permutation TE Sn with no fixed points, i.e. none of the elements remain in…

A: Introduction: Derangement is a very significant in combinatorics. Derangement is the process where…

Q: Discrete Maths Oscar Levin 3rd eddition 4.3.9: Prove Euler’s formula using induction on the number…

A: Given Euler’s formula using induction on the number of vertices in the graph.

Q: If positive integers are chosen at random, what is the minimum number you must have in order to…

A:

Q: Give a formula for the number of permutations of [n] with no cycles of length exactly 2. Your…

A: Formula for the number of permutations of [n] with no cycles of length exactly 2 is derived.

Q: Check all symmetries that apply. 27x +31y = 51 %3D Symmetry:

A: Symmetry: a) About y axis: If we replace x as -x and equation become same that is equation is…

Q: The distinct characteristic roots corresponding to the recurrence relation an=7an-1 -10an-2 are:…

A: The given recurrence relation is an=7an-1-10an-2. Rewrite the recurrence relation is an=7an-1-10an-2…

Q: 13. Is (Sn,) a commutative(abelain)? Is (Sn,) cyclic?

A: Solution is given as below :

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

A:

Q: 1. Find all cquivalent classes determined by congruence modulo 5 on Z.

A: The equivalent classes under modulo n is defined by, a=x∈ℤ: x≡amod nIn the question n=5a=x∈ℤ: x≡amod…

Q: Suppose that you have 3 and 8 cent stamps, how much postage can you create using these stamps? Prove…

A: We shall show that every postage >=14 can be created using 3 and 8 cent stamps. And then deduce…

Q: The distinct characteristic roots corresponding to the recurrence relation an=7an-1 -10an-2 are:…

A: Substitute the value of , we get

Q: pls explain to me step by step

A:

Q: Let a and ß belong to S,. Prove that a-'ß-laß is an even permutation. n°

A:

Q: Prove that peanos 5th axiom and principal of mathematical induction are equivalent

A: We have to show that Peano's 5th axiom and principal of mathematical induction are equivalent.

Q: How

A: Here use combination

Q: Show that a permutation with odd order must be an even permutation

A:

Q: Prove that if we move straight down in Pascal's triangle (visiting every other row), that the…

A: In any Pascals triangle nk, n≥k≥0 When we move 2 rows down and move 1 over then it becomes n+2k+1 we…

Q: Consider the pseudorandom number generator given in our lessons: with Uf +1 = (auf + b) mod m…

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Q: 4.] Find PIAJ if A = Co,bicd)

A:

Q: Find the inverse of 35 under mod 233(if exixts), by using Euclid's Algorithm?

A:

Q: Show that if E has finite i

A: To prove that if E has finite measure and∈>0, then E is the disjoint union of a finite number of…

Q: Solve the following DE Using Method of Undetermined coefficients; applying both (a) Superposition…

A:

Q: Consider the recurrence: an=0.5an-1 + n with initial conditions ao = 1. Then, the value of a200 is:…

A: we have, an=0.5an-1+nwhen n=1a1=0.5a0+1⇒a1=0.5+1⇒a1=1.5when…

Q: Find the number of inversions in the permutation 52134 of Sz = {1,2, 3, 4, 5}. 6 O 5

A: Number of inversions

Q: 8. Find a for and az geometric sequ E5103 and the 3D21 given

A: consider the geometric series   a , ar , ar2, ar3, . . .  where a1=a

Q: Find integers X, E > 2 such that XE = X (mod 74329). How does this illustrate a potential problem in…

A: Given :           E ≥ 2 such that XE ≡ X (mod 74329).   To find integer X.

Q: Consider the recurrence relation an 5аn-1 + 2n. If a1 = 6, determine the value of each of the…

A:

Q: Apply Taylov's expansion and find The seyies for tenn at 4

A: Taylor's expansion of tan2x at π4 Now fx=∑n=0∞fnan!x-an fx≈Px=∑n=0∞fnan!x-an Now derivation of given…

Q: Suppose Quark decides to be a little less greedy. He offers two membership packages. a Basic…

A: Question- Suppose Quark decides to be a little less greedy. He offers two membership packages. a…

Q: If C and D are two n ×n invertible matrice hen one of the following is always correct

A:

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

A:

Q: Give a recursive definition for the set of all binary palindromes, that only '0's and 'l's that are…

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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: O lim Sop of Sn= 61)" (24 ) is ?

A:

Q: For neN, is f(n) = "+) a solution to the recurrence relation 2 an = n+ an-1?

A:

Q: Find the Maclaurin serie: e2x

A:

Q: The Extended Euclidean Algorithm allows us to efficiently compute inverses in Z∗n (and also in…

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Q: Find all possible laupent Sepies expansion5 Of about the (z+1)(2) (Z-2) point zo =-1. %3D

A: Given: F(z)=7z-2z+1zz-2 By partial fraction, =1z-3z+1+2z-2 Put U=z+1z=U-1…

Q: = Solve the recurrence relation an an = an−1+2″ with að = 3.

A: The given recurrence relation  is  an=an-1+2n with a0=3. The objective is to solve the recurrence…

Q: : The Wronskian of e" , e2¤ Add a caption... > Status (Custom)

A:

Q: Show by means of a membership table that both absorption laws are identities.

A: According to the given information, it is required to show that the absorption laws are identities…

Q: Find the simpler circuits with the same output of the following sum-of-products expansion. xyz +…

A: We will simplify the following boolean expression.

Q: QUESTION 10 How many bit strings of length 6 start with 10 or end with 01?

A: By fundamental theorem of multiplication counting is

Q: 1. Determine if each of the linear congruences below is solvable. If a congruence is solvable, then…

A: The general form is ax≡b(mod m), first check is this linear congruence solvable or not? for that, we…

Q: Show that the permutation [n, n-1, ... , 2, 1] has n(n-1) inversions.

A: An inversion in a permutation is a pair of numbers such that the larger number appears to the left…

Q: Find the integer a, if the modular representation of a is (2, 1, 5) with respect to the modulo 3,…

A: We have to find the integer a if the modular representation of a is 2,1,5 with respect to modulo 3,…

Q: 7) Show that if a, > 0, and Lim na, +0, then the series aj + az + az + a4 + diverges.,

A:

Q: #2

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.