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

Q: Prove that (-1+ iE)" + (-1- i5" has either the velue 2n+! or the value -2" f ロ ww. š any integer…

A: The cube root of unity is written as:

Q: Find the identity element for the operation * on N defined by a *b=a+b+2, Va,beN al al a 240 does…

A: Let e be the identity element. Hence, it can be written that a*e=a .

Q: Ex: Let X₂ [1,2,3,4,5]. I. [0,X, [1], 82.3, 81.23], Y. [3,4,5,6,73 andl T₁: [0, X, [4], [4,633 if A:…

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Q: . How many Boolean functions are there of degree 7? Explain.

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Q: Determine the least upper bou You must fully justify your an

A: We have to find least upper bound of the given set

Q: Prove that (1 + x)n≥ (1 + nx), for all natural number n, where x > – 1.

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Q: 2. If a set X has n elements, how many elements are in the power set P(X), we exclude the empty set…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Prove C(n,0)=C(n,n)=1 for all whole numbers n

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Q: If fN is the set of the first 100 positive integers, A is the set of odd numbers between 50 and 90,…

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

Q: 15. m ZU 144 60° W

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Q: For every integer n such that 0 ≤ n 3n.

A: For every integer n such that 0 ≤ n < 4, 2(n+2) > 3n. So, n can be 0,1,2 and 3 For  n= 1…

Q: (a) Decide whether or not there is a simple graph with degree sequence [0, 1, 1, 1, 1, 2].

A: In first part we have given degree of sequence and in second part number of student. We have to…

Q: Explain why f e-a dx cannot be evaluated using u-substitution. Then give an example of a similar…

A: Consider the integral ∫e-x2dx. Suppose u-substitution is possible. let u=x2. This gives,…

Q: (1+ V5 (3 – V5) Without using a calculator, express in the form a+bV5, where a and b are integers.

A: The given expression is: 1+53-5-2 Express in the form a+b5, where a and b are integers. Rewrite the…

Q: a and b are positive integers, show that gcd(a,b) = gcd(a,a+b).  Discrete math questio

A: To prove that gcd(a, b) = gcd(a, a + b) for positive integers a and b, you can use the properties of…

Q: Lot f be ertine Rnd K be a positive integer Suppose that there are M70 and e7o ouch that 15(e)<M|2|"…

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Q: step by step in digital format XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Let A be a…

A: I have given the answer in the next step. Hope you understand that

Q: AV Prove that every integer greater than 6 can be written as 3x + 4y for nonnegative integers x and…

A: We have to prove that:Every integer greater than 6 can be written as 3x+4y for nonnegative integers…

Q: Prove:  C(n,k) = C(n-1,k-1)+C(n-1,k) for natural numbers k with 0<k<n.

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Q: y" + Oy' + ly = h(t – 12), y(0) = 19, y' (0) = 0 Use h(t a) for the Heaviside function shifted a…

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Q: Find all natural numbers m and n with properties GCD(m,n) = 8 and LCM(m, п) — 168. %3D

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Q: Negate the statement: For all positive integers, n, there exists a positive integer, k, so that…

A: The negation of a statement is:- Statement:- p implies q. Negation:- p does not imply q.

Q: 2. Almost! But there's nothing that maps to 0. In your notes at the top you've listed ℕ={1,2,3,…},…

A: Solution:  f : Z → N Consider f(x) = |x| Now, we see, f(-1) = |-1| = 1 and f(1) = |1| = 1 although…

Q: 3. Let n ≥ 9 be an integer. Give a combinatorial proof of the identity n-5 k n - () = (^=) ("=^). 9…

A: Here n&gt;=9 (Given )  n belongs to N There are 'n number of balls and We have to choose 9 ball from…

Q: x. State the Prime Number Theorem and give an explanation of its results. XI. What are Mersenne…

A: Prime number theorem gives an approximate value for the number of primes less than or equal to any…

Q: 1. Prove that for all positive natural numbers n,13 + 23 + ... + n3 = n2⋅(n+1)2/4

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.