x +1 0 0 64 0. Let A = 2 0 Find x and y if A3 = 8. 0. %3D 0 y, 0. 0 64 T = y = 00

Q: iii) True or False: Every subspace of a complete metric space is complete.

A:

Q: i) True or False: T = {0, R} U {(-o, a]: a € R} is a topology on R.

A:

Q: Q3 Give an example of a connected subspace of R2 which is not path- connected.

A:

Q: Discrete

A: Consider the provided question,

Q: Q1. Let X = {m,n, p, q}, {ø, X, {p}, {m, n}, {p, q}, {m, n,p}, {q}} and Y = {a, b, c}, F =…

A:

Q: Q7. Assume that (R,T) is the usual Euclidean topological space. N = {1,2, 3, ....} C R. Determine…

A: There is no interior point of N.

Q: Prove the following statement, using either the contrapositive statement or a proof by…

A: Proof by contradiction is done bellow

Q: Consider the equivalence relation on R defined by r ~ y if x – y € Z. Describe the quotient space…

A: In topology and related areas of mathematics, the quotient space of a topological space under a…

Q: Discrete

A:

Q: 4) Let 7 be the Euclidean topology on R and 71 be the discrete topology on R. Define f: (R, 71) →…

A:

Q: X be given by J(*) 2. Let X be the set of real numbers, let U be the usual topology, and let D be…

A: (a).         f : (X, D)  to  (X, U)   is continuous. Because if we take any set open in (X, U) ,…

Q: Let X be the set of reals, and let T = {SCX:0€ X-S} U {X}. Show that T is a topology for X and find…

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Q: Match the homeomorphic figures. ....F Prove or disprove the following: FA and R are pathwise…

A: Given:- (a)Homeomorphic figures     △.................. F  T.................. 0∞...................…

Q: Discrete

A:

Q: Let X be an infinite set with the countable closed topology T-{S subset of X; X-S is countable}.…

A: Given that X is an infinite set with the countable closed topology T-S subset of X; X-S is…

Q: Prove that v5 is irrational.

A: To prove 5 is irrational. Use the method of proof by contradiction.

Q: Use the given figure to find the following sets? A U B ВПС С - А A - B 2 A B 4 P. (В - С) U A (СП В)…

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Q: f(x) = {x + 2 if x > 1 (2x – 1 if x < 1 then f -'( ]2,4[ ) is then f-(]2,4[) is [1,2[ and f is not…

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Q: Q4 (a) Solve for x if 25x = 15(mod 29). (b) Determine the smallest positive integer so that when…

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Q: discrete

A: In method of contradiction we start by assuming that given statement is false. Then prove that it is…

Q: Discrete

A:

Q: Let (X, T) and (Y, T1) be topological spaces and f a mapping of X into Y. If (X, T) is a discrete…

A: For proving f is continuous enough to prove that inverse image of every open set is open.

Q: ii) True or False: The space R is homeomorphic to the closed interval [-1,1] with the usual…

A:

Q: Discrete

A:

Q: Which of the following sets is open in (IR, Tu)? OR-(Q-Z) (1)"2n? nin?:nE N} R - [2,5) O 12, 5) U…

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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.