Which of the following sets is open in (R, Tu)? OR-(Q-Z) OR-)"2n² :ne N} [2,5) O 12,5) U (1, 7) R-(()"2n :ne N}U{-1,1})

Q: If ftickiieI{ is acollechion of Subsets ofX then く) andh %3D det the equality not (X;)-( true in…

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Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: Thoorem: is not closed set

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Q: Show that the mogping LiPaRI-+IR L Carcaxtat = (asta, on) is liher trasfaret

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Q: Let (R,r) be topological space with usual topology on R, then the set Qof rationals is O Neither…

A: ℚ is the set of rational numbers. ℝ is the set of real numbers. So, ℚ is a subset of ℝ .        i.e.…

Q: 2. if it was P(x)=ao+a,%tazk Prove that PecR) inner multiPlication sPace

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Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: 8. In a university examination, which was indeed very tough, 50% at least failed in "Statistics",…

A: P(failed in Statistics) = 0.50P(failed in Topology) = 0.75P(failed in Functional Analysis) =…

Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: 15, If neZ, then nº +3n +4 is even. (Try cases.) ho bn 6. If two integono

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Q: => find fundamental set of Se yo=-3x²e-3x ZR 7:

A: We have to find the fundamental set of solution.

Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

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Q: Prove that ifS is a bounded set, then inf(S) = -sup(-S) %3D

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Q: Determine for which n ≥ 3, Wn has a Hamilton circuit. Justify your answe

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Q: It was found that 33% of all diners order vegan meals and that 90% of all diners are undergraduate…

A: The following information has been given: Let us consider "V" denotes the event diner orders a…

Q: The equivalence class of -2 for the relation congruence modulo 5 is о (... -11, -6, —1,4, 9, 14,…

A: Second option is correct.

Q: Give 3 different examples of norms on Z (set of integers)

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Q: Please solve 4,5,6,7 The Borel o-algebra on Ris generated by any of the following collections of…

A: As per the company policy, in a multipart question like this, we can solve only the first two…

Q: Show that gcd (f1,..., fa) = gcd ( f1, gcd (f2, ... , f,)) for any s > 3.

A: The greatest common divisor of two numbers a and b is the number that divides both a and b. It is…

Q: Show {5, 10, 15, 20, - - ·} is countable. (Hint: Use the function f(n) and onto). = 5n and show it…

A: 4 Given set is 5,10,15,20,....... We have to show that the set 5,10,15,20,...... is countable. Let a…

Q: 3. Prove or disprove: U(8) Z.

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Q: SUppose K,n EZ and O < Kcn. Prove +hat by (onsi nsi dering subsets of (1,... --- --- (^) - (":') + (…

A: The given problem is to prove the following identity using the basic mathematical identities.

Q: 4. Show that if A is closed in Y and Y is closed in X, then A is closed in X. Verify it and make…

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Q: A and the set B = {x, y}, then A X B is denumerable as well.

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Q: (4.2) Let X = {1,2, 3, 4} and 7 = {0, {1,2,3} , {2, 3},{1},X} be the topology defined on X. (a) Show…

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Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

Q: How many funcei ons F{,2,3,4is}→ {l,2,3} are ehere eien er FCI)=1, F(2) 2, f (3) =3? or

A: To find the number of function f such that either f(1)=1 ,f(2)=2 or f(3)=3 .

Q: (a) What is the cardinality of the interval (0, 1), finite, countably infinite, or uncountable? (b)…

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Q: Prove or disprove that if {a,} and {b,} are Cauchy and b,n # 0. Then An is Cauchy

A: If an and bn are Cauchy and bn≠0, then anbn is not Cauchy. Result used: If an and bn are Cauchy and…

Q: 1. Prove with the resolution calculus -(PA-Q) -P (RAS) VQ

A: To prove with resolution calculus: ¬P∧¬Q         ¬¬P__________R∧S∨Q

Q: Deteimine the set of vectuns sci, iti), (1tiyzi)f linealy dependent or linenly Indefendteut? is

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Q: Let Az = { k, k + 1, ..., k²}, for k 1,2,3, .. Find U은1Ak-nE1 Ax

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Q: (a) What is the cardinality of the interval (0, 1), finite, countably infinite, or uncountable? (b)…

A: Schroder-Bernstein Theorem: If there exists injective functions f : A→B and g : B→A between the sets…

Q: Let ū, ů ů be VCctors in a real inner Product spale, with cŮ, w) = -3 (ů,3) =5 ニ 11ů-20112 -(25, ) =…

A: Given: u→.v→=2, v→.w→=-3, u→.w→=5, u→=3, v→=2, w→=2 we know that u→-2v→2-2w→.w→ is given by…

Q: let t={usx8 x-uiscoantableiuioi then Tis called Tcof

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Q: 3. Suppose (a,n) is Cauchy and that for all m, k 2 100, Jam - as 0. Does it follow that the…

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Q: ind the all possible number of different multi sets of size '4' from -element set, in which at least…

A: In this question, the concept of permutation is applied. Permutation Permutations are frequently…

Q: 2 FIND THE PARAMTRIC AND SYMMETRI C EGUATIUNS OF THE LINE THAT PASSES THROUGH (2,8,10) AND く2,8,147…

A: The given data is: The line passes through 2,8,10 and parallels to 2,8,14 To find the parametric and…

Q: Prove disprove that (R.Tco-finite) is Te-space or

A: To Prove - Prove or Disprove that ℝ, τco-finite  is T2 - space.       Definition used - T2 - space…

Q: 3. Let, a, = 3, az = 4 and for n2 3, a, = 2a,-1+ an-2 + n² + 1, express a, in terms of n. %3D

A: Recurrence relation - it  is an equation that denotes  the nth term of a sequence as a function of…

Q: Let S = {0, 1}. List all the strings of length 4 over S that contain three or more 0’s.

A: It is given that S = {0,1}.It is known that if n be the positive integer and given a finite set A,…

Q: The set {u1, u2, u3} is orthonormal. 1 2 V5 V5 1 2 1 2 10 ,U2= ,u3= 10 1 2 1 2 10 10 True False

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Q: (1) Write the Cauchy theorem (without proof).

A: Dear students you have asked multiple question, as per our policy your first question will be…

Q: Is f(x, y, z) = 8 In x+7 In y+5 In z homothetic? Of(x, y, z) is not homothetic Of(x, y, z) is…

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Q: set of integers is denoted by Z

A: There is some standard notation for certain types of sets . Set of real numbers is denoted by R,…

Q: Let X = {a, b, c} and R={(c, b),(a, c)}. Then Check the all properties reflexive,symmetric,…

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Q: 4.2 Let Fj, be a closed set for k = 1,2, ... ,n in (S, d). Show that U Fk is closed.

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Q: uppose (X,≺) is a well-ordering. Then (X,≺) is not isomorphic to (pred(X,≺,x),≺) for any x ∈ X.

A: Set theory

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.