tind the east uprer bound of the set A ntl nE INZ in Q. Prbue that this vaue iS an upper bound and that it is, in fact, the least upper bound.

Q: Let T = {x, y}. List all the strings of length 5 over T that have exactly one y.

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Q: Q) prove that aset A is non denumerable iland only if AxAXA is nondenumerable

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A: Solve the following

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A: According to the given information, it is required to prove that:

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A: The sine distance between two points x,y∈ℝ2 is defined as: dsinx,y=x.yxy and the cosine distance…

Q: Prove that, there is no simple grcup of order 200.

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Q: Let S be a non-empty bounded subset of R and let a be an upper bound of S. Show hat sup S = a if and…

A: Follow the steps.

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Q: Let W be a nonempty subset of R that is bounded above, and define the set B as follows B= {N ER:N is…

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Q: Find the Velumme of the Sotids abtaind Yegion in the first quadrand bound by Hhe Cerves Y=2- x² by…

A: We will draw a region first then using Integration, we will find volume of solid

Q: prove that an is bounded above.

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Q: (a) Let S {2 ringleton is open set in (M, d). oce and let ACM. Prove that aA = O if and only if A is…

A: The problem is from Topology.

Q: . Let S be a bounded set in R and let T be a nonempty subset of S. Show that inf S <inf T< sup T <…

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Q: Let M and N be nonempty bounded subsets of R and let M + N := {m + n : m ∈ M and n ∈ N} . Prove that…

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Q: If S is bounded subset of R, then supS E S. Select one: O True O False

A: The given statement is     If is bounded subset of , then .

Q: a) Prove by the principle ofF mathematical #hat Inductio n that (ab)" =a" bn is true natural hunmber…

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Q: of points of S. 6.30 Show that a set consisting of a finite number of points in E is bounded. Gnita…

A: Given, a set consisting of a finite number of points in E.

Q: Let S be a non empty subset of R and let u e R be such that u + is an upper bound of S for each n e…

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Q: If S and T are nonempty bounded subsets of the real numbers, show that if ScT Then infT < inf S <…

A: Given ,  S is subset of T

Q: Consider the subset T = {r €R: , <0} of R. x² –3x 3.1 Express T in interval notation. 3.2 Choose ONE…

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Q: Every non-empty subset of Z has a least element. Select one: O True O False

A: Given ℤis a subset of integers Clearly , the set of even integers is a subset of ℤ Set of even…

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Q: 5. Show that the set {e" : n e Z} is countable. (Hint: Use the function f(n) = en and show it is 1-1…

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Q: Suppose that S is a nonempty subset of R and k is an upper bound of S. The number k = sup S if and…

A: Given: S is a non-empty subset of R and k is an upper bound of S. To prove : Number k=sup S if and…

Q: 3.) Prove that P, is a all ve ctor by showing space 10 0xioms ore

A: proof P2=a0+a1x+a2x2:a0,a1,a2∈R   is vector space over + and ×first we proof P2 is abelian group…

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Q: If A and B are bounded subsets of R, then AuRand AOR are bounded: prove that

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Q: 2.12 let A and B bounded sets For which there is an ε >o such that la-blze for all ac A, be B .…

A: Consider A and B are bounded sets.

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Q: Let S be a 50-element subset of {1, 2, 3,...,87} and let T = {s+11 :sE S}. Prove that SnT+ Ø.

A: This is a question of Set theory, application of the Pigeon Hole Principle.

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Q: Prove that the set S = {n² : n E N} is denumerable.

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Q: Prove that sup(A) =1, inf(A) = . 5. (i) Let A, BCR be sets which are bounded above, such that AC B.…

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Q: Let min EN 7 atZ be such theut Ca,m)=1, Ca,n)=| ¥ min)=\, Let K = Om (a) I j= On(a). 31K that ak=I…

A: Given that m,n∈ℕ and a∈ℤ with a,m=1, a,n=1 and m,n=1.  Suppose  k=Omaj=Ona With j|k To prove that…

Q: Let S be the congruent modulo 7 relation on Z, that is m Sn 7|(m-n). Show the relation S is: (a)…

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Q: in extension of a fie elements in K which ver F from a subfie

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Q: Define u* on the power set of R by Jo if A is bounded, 4*(A) = 1 if A is unbounded. Is u* an outer…

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Q: State whether the given set E is bounded or unbounded and justify your answer with a proof. E = {z €…

A: We are given the set, E = { z ∈ Z : z ≡ 7 mod 9}. First, we will try to find the elements in E then…

Q: Label each of the following statements as either true or false. The least upper bound of a nonempty…

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Q: Apply any method to prove that alb (or a nand b), which is defined to be ¬(a ^ b) is complete. Write…

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Q: Let A be a nonempty subset of R that is bounded below. Define the set B={b: b is a lower bound of…

A: Given A is nonempty subset of ℝ. Also, A is bounded below. Greatest lower bound property: The…

Q: . Let S be the congruent modulo 7 relation on Z, that is m Sn 7|(m-n).Show the relation S is: (a)…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.