Define the closure of a sot I in a motric spack. How is the boundry it a sut I related to it clogwai

Q: Discrete math.  Let S = R. On S we define the relation R as follows (∀x)(∀y)(xRy ⇔ y ≥ x + 3). Is R…

A: The given set S=ℝ. The relation R defined in the set S is ∀x∀yxRy⇔y≥x+3. We have to check whether…

Q: Is H=eQ funation homo the tic function (Here, s = AK

A: Homothetic function A function ν:ℝn→ℝ is called homothetic if there exist a strictly increasing…

Q: Let A be a non-empty set of real numbers which has a upremum and let B= {x : - x e A}. Show that B…

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Q: friove it with atleant one one esuanple thein aLccb

A: we have to give one example of each of given integral identities. a)if a<c<b…

Q: $hOw th@t the follOwing sets are not regular using pumping lemma 1. { wwR x | w, xi{a,b}*} (d}{ xwwR…

A: Show that the following sets are not regular using pumping lemma: Where x and w are the strings. wR…

Q: Assume that A and B are nonempty, bounded above, and satisfy B CACR. Show that sup B < sup A.

A: Introduction: The supremum and infimum properties are the very important properties of any subset of…

Q: Let A be a nonempty subset of positive integers and B = {n + v5 : n E A}. Show that B has a least…

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Q: Then slouw that E Alasf bea, Couly, seguene in D. is also Cauchy.

A: Here uniformly continuous is necessary condition. Here is proof.

Q: Let f : A → B be a function, {B;}jej a family of subsets of B. Prove that f-'(Njej B;) = Njej…

A: Given that f : A → B is a function. Also given that Bjj∈J is a family of subsets of B . We have to…

Q: Shafe froe fabe, oting your ener. or The sef of natural nurnkers Bith the cwuel metir is compact of…

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Q: Exercises for Sets and Functions Q1) How many elements does each of these sets have? b. P(Ø, {Ø),{Ø,…

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

Q: Exi Find of the A line of intersechion. egns of the 'two planes

A: Solve the following

Q: Let N R R be any norm on Rn. Show that N is a convex function (give all the details for the proof).

A: Given N :R^n→R be a norm on R^n.      To show : N is a convex.     Definition of norm :…

Q: IF Function F is bounded on [a,6], does F has as abs ,max and abs. min not ? or

A: We have a example such that that is bounded but not attains either absolute maximum or minimum.

Q: Ex(ia)g prove or dis prove that Ris equivalance relation on x iff Rtis equivalene relakion ony

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Q: Prove that if R: R -> R is continuous, theis b2n the image of a bounded set over f is bounded

A: As per the question we have to prove that if any function f : ℝ → ℝ is continuous, then the image of…

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}.…

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Q: Find the null space for A = 1 2 What is null(A)? {(} O A. O B. R? {} O C. span O D. span: 2 2. O E.…

A: We have to find the nulllspace of the given matrix .

Q: d) i = 1

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Q: The set X is an open set in the ambient metric space . O True O False

A: Solution

Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

Q: Find a Linpar O peretor L with null Space (kernel)

A: We have to find the linear operator L with null space(Kernel) nL=excos2x,exsin2x

Q: Punctian diffexentiable Af not Is every in tegsable. by then prove it giving countes example.

A: No, every differentiable function is not Integrable. Consider the function f(x)=1x  in (0,1). Obtain…

Q: 15 - Let f be the function f: A -> B. A, B and f are defined as {1, 2, 3, 4} {5, 6, 7, 8} f = {(1,…

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Q: Suppose that 0 0. Prove that there is an open set O containing E such that 0m* (0) ≤m* (A) and an…

A: The outer measure m* is a way to assign a non-negative value to any subset of the real numbers that…

Q: Convert the grammer s tentsto asb|bsa|a|b into greibach normal form

A: Given: S→asB|bsA|a|b

Q: 3.

A: Definition of Riemann integrable : Let f: [a,b] -&gt; R be a bounded function such that the upper…

Q: n Question 3 For the relation R on the set of integers, where xRy if x is a factor of y, select all…

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Q: 5. (8 points) Let S4be the set of all strings of 0's and 1's of length 4. Define F:S4 → Znonneg such…

A: The objective of the question is to understand the properties of the function F defined on the set…

Q: List the ordered pairs in the relation R from A=0,1,2,3,4, B= 1,2,3, 4, 5, where Ris defined as (a,…

A: Given sets are: A={0,1,2,3,4} B={1,2,3,4,5} Relation R consist of those ordered pairs (a,b) such…

Q: Let R (the set of real numbers) be equipped with the Euclidean topology and let S = {O, 1, 1/2, 1/3,…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: A⊂B, prove that if B is bounded, then A is also bounded. Is the converse true?(

A: Let A⊂B, where B is bounded. Then there exist two real numbers k and K such that k ≤ b ≤ K for all b…

Q: Assume X = (1,3,5,7}, Y = (1,9,25,49)} and F(x) = x2, such that F:X Y. Then the following is true…

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Q: Functions that are both one-to-one and onto are also known as A inverse B injective c) bijective (D)…

A: The functions that are both one to one and onto are known as

Q: 7. Use set identities or different proof method to show that: (AUBY NA = Ø

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Q: Consider the subset R = R × R − {(x, x)|x ∈ R}. What familiar relation on R is this? Explain.

A: Concept used: Subset relation Subset relations are used to define partial orderings on sets. A set's…

Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…