If A is a perfect subset of B and P(a < P(b)), then P(B - A) is equal to Select one: O A. P(b) - P(a) O B. P(a)P(b) O C. P(a) + P(b) O D. P(a) / P(b)

Q: Suppose that there are 6 people in a room. Show that one can always find a group of 3 people such…

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Q: 2. Let A Ø. If A has exactly n elements, then A has exactly 2" subsets, Vn € N.

A: A is non empty subset of n elements ,then A has exactly 2n subsets,∀n∈ℕ.

Q: In group of 6. Each 2 of them, hate or like each other. Proof that there are 3 who hate or like each…

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Q: (c) 2, 3, 4+ V10 and 4. V10 are irreducible elements of R.

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Q: (iv) The power set P(C) of C by listing down the elements directly.

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Q: 1 Decide the behavior (AC, CC, or D) of . n=2 nVln n

A: Given: ∑n=2∞1nlnn, Here f(n)=1nlnn. Calculation: Intergal test states that "Suppose that f(x)&gt;0…

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2, express a, in terms of n.

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Q: Prove: |P(A)|= 2" where |A| = n. (Here P(A) is the power set of the set A with n elements.)

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Q: inf a, + inf b, <inf(a, + bn), sup(an + bn) < sup a, + sup bn, n n

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Q: 3. A service station has both self-service and full-service islands. On each island, there is a…

A: Introduction:  The joint PMF. The joint PMF is the tabular arrangement of the probabilities of each…

Q: There are n = 50 students registered for the course 08TI2. It is well known that two students are…

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Q: Prove that if r <s < n, then P(n , s) is divisible by P(n,r).

A: Given: r≤s≤n Therefore, n-r≥n-s So we can write n-r! = n-rn-r-1n-r-2...n-sn-s-1n-s-2...1 n-r! =…

Q: A group of n = 2k people enter a 2-on-2 basketball competition. Before the competition starts, the…

A: In this question we have to find a relation to find number of teams.

Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

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Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: A customer ordered eleven zingers. Zingers are placed in packages of four, three, or one. In how…

A: A customer ordered 11 zingers. Zingers our placed some packages of four, three, or one. How many…

Q: Show that A5 has 24 elements of order 5, 20 elements of order 3, and15 elements of order 2.

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Q: Show that if P(A;) = 1 for all i > 1, then P(N1 A¡) = 1.

A: We know that P(Ai) = 1 for i ≥1 Considering P(Ai), i=1,2,3,... to be independent events

Q: Find (a) K (b) CDF of X

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Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

A:

Q: Show that A5 has 24 elements of order 5, 20 elements of order 3, and 15 elements of order 2.

A: We know that A5 has only even order permutation. A5 has 5!2=60 elements. Now write the partition of…

Q: uppose that A ⊆ C so that n(A) = 5 and n(C) = 11. How many subset B, with n(B) = 8 are there such…

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Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a,= 2an-1+ an-2, express a, in terms of n.

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Q: Prove that if r < s < n, then P(n, s) is divisible by P(n.r).

A: Use the formula of permutation

Q: (e) There exist subsets A and B of N such that (A-B) n (ANB) = TRUE FALSE

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Q: 1. Find the number of strings of n (not necessarily different) lower case letters from the English…

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Q: If 90% of x is 8100 then x is

A: Given,         90% of x is 8100.

Q: a) What is the maximum possible order of an element in S,? Give an example of one of these elements.…

A: Given, Group S7 any element can be written in cycle notation i.e. in disjoint cycles as example…

Q: O cf AandB are subsets of X such that A=R 3. then fiA = {cB but the converse is not tiug

A: Let A and B be subset of X and  let f be function from A to X If A=B =&gt; f(A)=f(B)   taking both…

Q: Consider the reduction from 3-CNF-SAT to SUBSET-SUM. For the formula ϕ = (x1 ˅ ¬x3 ˅ x4) ˄ (¬x1 ˅ x3…

A: Given, Formula ϕ = (x1 ˅ ¬x3 ˅ x4) ˄ (¬x1 ˅ x3 ˅ x4) ˄ (¬x1 ˅ x2 ˅ ¬x4) and Clauses C, C1 = (x1 ˅…

Q: b) Use generating functions to determine how many four element subsets of S = {1,2,3, ..,15}…

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Q: 2. A group contains k men and k women, where k is a positive integer. How many ways are there to…

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Q: (9) The set of all prime elements in ({a + vZ b: a,b € Q}, +,.) = %3D ...... (a) Q (b) Q × Q (c) Ø…

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Q: (9) The set of all prime elements in ({a+ v2 b:a,b € Q}, +,.) = ... (a) Q (b) Q x Q (c) Ø (d) No…

A: Option (c) is correct...

Q: 22.17. In an analysis of two attributes, if: N= 160, (A) = 96 and (B ) = 50, find the frequencies of…

A: We want to find the all attributes.

Q: (a) How many arrangements of the letters in COMBINATORICS have no con- secutive vowels? (b) In how…

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Q: 5(a) Evaluate dr, by using 1) Sumpsom" rule W Simpsen" 3 fule.

A: Simpson's 13 rule uses the formula below to approximate an integral in an interval.…

Q: The five most common words appearing in spam emails are shipping!  today! here! available, and…

A: Probability of an event gives the chances of event happening. The probability value can be from 0 to…

Q: a) How many maximal elements does P have? b) How many greatest (or maximum) elements does P have? c)…

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Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

A: It is mentioned that 1 in every 10 messages is spam. Hence, the probability that the message is spam…

Q: If P(n) is the statement "n' + n is divisible by 3' Prove that P(3) is true but P(4) is not true.

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Q: Consider a group of n warehouses in a shipping network, where n>=2. In order to ship products across…

A: Here in the question it is given the number of warehouses in a shipping network having a set limit…

Q: ) Solve the problem by combinatorics .How many different strings can be made from the letters in…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Suppose that X is a subset of Y, such that P(Y)>0. Is true or false that P(X|Y) is equal to…

A: It is given that X is a subset of Y This means that PX∩Y=PX...(i) The formula for PX|Y is given by:…

Q: Suppose that there are n = 2k teams in an eliminationtournament, where there are n∕2 games in the…

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Q: he five most common words appearing in spam emails are shipping!, today!, here!, available, and…

A: I have provided solutions for first 3parts...as per Bartleby guideline!

Q: Suppose that A = {1,2,3,4} and P(A)is the powerset of A. Then |PKA)| =..?

A: We will use the formula.

Q: 6. If k divides |G| then 3H ≤ G such that |H|=k. *True *False

A:

Q: 3- Consider two evenbs A and B such that pra) = And PCB)= } Delermire p(AN B) For each of the…

A: P(A ∩Bc) = P(A) - P(A∩B)

Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.