Let S = (x: (x - 1)² = 0}, state where S is singleton set or not.

Q: 4. Give an example of a non-measurable subset of R. (witheutProof)

A:

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is F open?

A: A set is open if and only if it contains all of its limit points. Also recall that the union of open…

Q: A string of Lcoincides with the interval 0, L

A: Given, A string coincides with the interval on the . We have to set up the boundary value problem…

Q: does not exist

A: Given that:  The limit   lim(x,y)→(0, 0 ) x2 + yx2 + y2   .

Q: ) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.

A:

Q: II. Show that if preferences 2° € X*. strictly convex, then A'(xº) is strictly convex for each are

A: Use the preference criteria to prove the following. Show that in each case, they are convex.

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: Let S = Span}( 3 2 3 . Show that dim(S)=2. 3

A: Basis: Let V be a subspace of ℝn. A basis of V is a set of vectors v1, v2, ..., vm in V such that:…

Q: What is the class width (i) if one of the class interval is 18-26?

A: If class interval given is 18-26 The class width is difference between upper interval and lower…

Q: 24. State if the following is discrete or continuous. "Number of blades of grass on a soccer…

A: Discrete: Discrete values can take whole number values within a permitted range. Example, Number of…

Q: 5. Let S be a set of negative numbers. Prove the least upper bound of S cannot be positive.

A: To show that the least upper bound of a set of negative numbers cannot be positive.

Q: Calculate the class interval of the class 0-30: 15 30 No class interval

A:

Q: every interval is path-connected

A:

Q: Create the logic circuit diagram for F= XY’ + XZ

A: Given problem Given that   F= XY’ + XZ

Q: Find the expontial functhion that passes through the points (2,6) and (3.1)

A:

Q: If x>-I show Hhat Cl+x)> \+nx ,H

A:

Q: Suppose that fa f (uniformly) and gn= g (uniformly) (pointwise) on A CR. on a set ACR. Show that…

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

Q: The continuous image of a connected set is connected. That is, if X is connected and f : X–→ Y is…

A: We prove this via contradiction. We assume that f(X) is not connected then X is not connected. And…

Q: What is the width of the class interval of 1-3?

A: Width of the class interval

Q: Let f(z) be an ODD fanetion. If the point (2,3) belongu to f, then another point likely to (0,0) (2,…

A: Given f(x) is odd function.

Q: Define degrees of freedom in the context of t-tests

A: Determine the degrees of freedom in the context of t -test. T test: The t test is used to check if…

Q: example 3.19- for any set ax we may defined the function X x X -> X by function (u,v) = u. In…

A: The given question is solved below.

Q: Express (4, 10) as a set {x : |x − a| < c} for suitable a and c

A: Write the given interval in inequality form as follows: 4<x<10

Q: Use the listing method to express the set S = ((1,3] x {2,4}) n z².

A: Given, S=(1,3]×{2,4}∩ℤ2 We have to express it in the Listing method, As we know, ℤ2=(a,b) where…

Q: Is the set X is linearly dependent or independent X = {(1,0,1,0), (0,3,0,1), (1,1,2,2), (3,4,1, −2)}

A:

Q: 3. What are the restrictions on x?

A: It is known that side length cannot be negative. This implies that, 3x+2>03x>-2x>-23 First…

Q: A relation R defined on the given set A will satisfy

A:

Q: 5. Prove that if ƒ : [-1, 1] → R is measurable, then |f| is also measurable.

A:

Q: IF f:x-у and vCy proof fy/v)=x/f"(v) and proof f is continous iff f'(E) is closed set in x for every…

A:

Q: If minimum observation is 46.8 and maximum observation is 192.4, number of classes is 6, then the…

A:

Q: 1- Find the set of lower bounds and the set of upper bounds of the following sets in R, if it…

A: Since you have posted multiple sunparts of a question so according to our guidelines we will solve…

Q: jim has precisely 150 followers. and, all 150 people who follow jim have precisely 150 followers. In…

A: Given that Jim has 150 followers and a follower of Jim follows Jim and 149 others. Let the set S is…

Q: Show that Let ECR" is measurable set. If µ(E) >0, then E have a non-measurable subset

A: Here, we introduce the notation Gr :=G∩[0, r) + 1-r ∪ G∩[r,1) - r for G⊂[0,1) and r∈R. Note that…

Q: Can you show an example of Null space?

A:

Q: Let F be an event space. Show that F is closed under countable intersections.

A:

Q: Let S be a nonempty set of real numbers that is bounded from above and let x = sup S. Prove that…

A:

Q: Let S be a set of negative numbers. Prove the least upper bound of S cannot be positive.

A:

Q: 6. Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below…

A: (i). Let  S = { ..., -5, - 4, - 3, - 2, - 1 }

Q: find the class interval for a class 6-9

A: Upper limit=9, lower limit=6

Q: It was noted that the binary propositional operators, A and V, can be regarded as functions, f: B x…

A: For any binary operator, number of rows in the truth table =4 Each row can have either True or False…

Q: EX LeT X = {!,2,3,415,6} T- Ex,¢,てり,E4,しろ4), [ス456 Topology.?

A:

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is F closed?

A:

Q: Let the non-empty set S = {x - yv3:x,y ER}, show that S is closed'under multiplication then find the…

A: We have to show that the given set S=x-y3:x,y∈R is closed under multiplication and also find the…

Q: FIND: The set, A, of critical numbers of f.

A:

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

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: Given the class interval 78.49 – 86.72, the class mark is Blank 1, the class size is Blank 2 and the…

A: Given 78.49 - 86.72 The definition of the class boundary is:

Q: Let X and Y be two discrete spaces, then *

A: Note: Since you have posted multiple questions we are only allowed to solve the first one. Thankyou…

Q: Show that if E is any measurable set, then -v (E) < v(E) < v*(E) and |v( E)| < \v|(E).

A:

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”.