28. Let R be a collection of sets defined by R = {x | x ¢ x}. %3D (a) Show R is not the empty set. (b) Is R an element of itself?

Q: 2. Use an edge-counting argument to show that K, cannot be drawn on a 2-holed torus without edges…

A: Suppose K9 had a 2-cell embedding in the torus. Then, this embedding has v=9 vertices and…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: 5. Let E be a set that bounded and c > 0. Prove that sup(cE) = -c inf(-E) %3D

A: This is a problem of Real topology, metric topology.

Q: Construct the intersection graph of the following collection of sets: 4 = {0,+2, 14, 16, ±,..} A, =…

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

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Q: The set S = {x | x is a continent}. A. S = {N. America, S. America, Europe, Asia, Africa, Australia,…

A: Given:  ( The set S = {x | x is a continent}  Then write the set S

Q: 9. If (X, M, ) is a measure space and E, FEM, then μ(E)+μ(F) = μ(EUF)+ μ(EnF).

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Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: d) Let X,Y, Z be sets. Calculate |XUYUZ if |X| = 50, [Y|= 90, |Z| = 71, |XnY| = 8, |Xn Z| = 9, |Yn…

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Q: If E <R, then for any 0 <E or an open set there exists b such that m * (G – E) < ɛ. Give an example…

A: For any non measurable set E, the above relation does not hold. The Example of such non measurable…

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: How many proper subsets does the set T={h,f,k} have

A: A set is given by, T = h, f, k. The objective is to find the number of proper subsets the T have.

Q: 5. Give an example (by words) for a collection of objects which is not well defined

A: Given, We have to write an example for a collection of objects which is not well defined.

Q: 21. Let A and B be two non-empty bounded sets of positive numbers and let C = {xy : x e A and y e…

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Q: 4) State the condition for equivalnce for measurable set. being a lebesgue

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

Q: 4,P) is a aɔnds (a) The intersection of any collection of closed sets in X is closed (in X). (b) The…

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Q: Identify the type of set (finite, infinite or empty) as described by the following: 1. A = {stars in…

A: A set is said to be finite if it contains only finite number of elements. A set is said to be…

Q: 5. Let (X,T) be a discrete space, then Va E X, the set {a} is а. ореn b. closed c. clopen d. is…

A: Let (X, T) be a discrete space.

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: A set SCR" is bounded if there exists k €R such that, for all x E S, || = VE, 0. What can you say…

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Q: 4. Find the following sets, which are subsets of R2. (a) U {a} x [0,1], (b) N {a} × [0,1], aeR aER…

A: Note: According to Bartleby guidelines; for more than three questions asked, only the first three…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: _1. It is a pictorial representation of the relationships between sets wherein the sets are…

A: Since you have posted multiple questions. We will solve first question. If you want the other…

Q: (10) Show that the set A = {a € Q : a² < 2 or a < 0} is a %3D cut.

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Q: 17. Which of the following accurately defines the complement of a given set, say A? A. {x|x€U and…

A: Complement of any given set is defined by all the elements in the universal set U which do not…

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To prove that the given fuzzy set is convex and to determine the α-cut sets for the given values of…

Q: List the elements of set D = { x:x є N, x is a multiple of 5} where N= {1, 2, 3, ...}.

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Q: will be prepared using i= 0.5, the lowest clas 18. The true limits or the class boundaries of the…

A: 18 From the part 17, the lowest class interval is (6.4, 6.9).

Q: ) Suppose X = {1,2, 3} and Y = {5,6). The number of elements of the set P(X × Y) = %3D

A: Number of Elements in Power Set P(A) of set A with n elements is 2n

Q: 4) Describe the graph of the given set C o{ (x,y): ニ

A: Parametric curves: When we define the coordinates of the point x, y in terms of another variable,…

Q: Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤…

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Q: Let S = {(x, y) E R X R: y - x = integer} List of four members of [-3]

A: GivenS=x,y∈IR×IR: y-x=Integernow-3=x∈IR: -3-x=Integernow, 1∈IR,2∈IR , 3∈IR and 4∈IRso the four…

Q: Give an alternative description of the sets specified below. 1. {x ∈ R : x^2 = 1}. 2. {x ∈ Z : x >…

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Q: A set consisting of single point has measure zero .A O nonzero measure .B O open .C O none of…

A: We have to find the measure

Q: Let'Y be the set of f bleod types B+ Hat type Connot donate blood to.

A: Here, X is the set of blood types AB- can donate blood. AB- can donate blood to AB- and AB+ Hence,…

Q: has

A: We have to choose the correct option from the given options according to the given information

Q: (a) The intersection of an arbitrary collection of closed sets is closed. (b) The union of any…

A: (a) We have to prove that the intersection of an arbitrary collection of closed sets is closed. Let…

Q: let A Set bounded below, ילC erove that C. nf A inf C A %3D

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Q: 5. Let (X,T) be a discrete space, then Va E X, the set {a} is а. орen b. closed c. clopen d. is…

A: Our objective is to choose the correct choice

Q: 7. Suppose that a set X is equipped with the finite closed topology. Which one of the followings is…

A: As per the policy, we are solving first question. Please repost the question and specify which…

Q: 5. Differentiate with respect to x: SET A. 5e

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Q: Let {Ek}k=1∞  be a family of pairwise disjoint measurable sets. Then show that A satisfies m*(A∩(…

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Q: Show the following set is convex. x≤10 [(1+(x-10)-²)¹ x>10 Determine a-cut sets of the above set for…

A: To show that the given set is convex: μAx=0                               x≤101+x-10-2-1  x&gt;10…

Q: In a bag of 350 chocolate candies, 37 of them are brown. The candy company claims that 13% of its…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

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?

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Q: ave a class boundary that is less than zero?  On the probelem I am working, the class goes from 0-5

A: Class boundaries are the values which help in separating the data points in statistics.

Q: 2- Moke the definitions of open and closed sets. x =Larbic,d,eļ and ノ closed subsets of (x,T) space,…

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Q: 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded…

A: part(a) GIVEN μAx=11+x TO SHOW: given function don't satisfy the following laws 1) law of…

Q: If the class boundaries are 16.45 20.55, then the class interval is ......

A: Class intervals is given by 16.50 - 20.50 Then we get class boundary as  (16.50-0.05)  -…