Write out the indicated sets by listing their elements between braces. Suppose the Universal set is a set of all objects, including all possible sets , and A = {a, b}, B = {1, {2}}, C = {Ø}. Show vour work.« а. (Ах С)xВе b. power(A) - power(C)- с. AUB-C'e

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: Thoorem: is not closed set

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Q: i. PROVE THAT THE EXCLUDED POINT TOPOLOGY ON ANY SET WITH AT LEAST 2 POINTS IS NOT HAUSDORFF. ii.…

A: Definition: A topological space X, τ is said to be Hausdorff if for every x, y∈X there exits U, V∈τ…

Q: cises Using just membership funchion for the following fuzzy sets. (of Course, you must first…

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A: Introduction: A set of disjoint subsets of another set. The original set must be equal to the sum of…

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A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

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A: NOTE: Refresh your page if you can't see any equations. . the polar coordinate  can be represented…

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A: The union of two sets is composed of elements of the same two sets.

Q: 2- Every finite set in any topological space is a- Regular set, b- connected set, c- Hausdroff' set,…

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Q: Show

A: We prove this statement by using definition of Borel Set.

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

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Q: Denote the set using the listing method {x| x is reciprocal of a positive odd number

A: The set of positive odd numbers are as follows: 1,3,5,7,9,11,13,15,17,19,21,23,……… Given a real…

Q: Fill out the Venn diagram using the given information.  |X|=40, |Y|=28, |Z|=38,  |X and Y|=15, |X…

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Q: Express the set using the roster method. the set of natural numbers less than or equal to 6.

A: Given: the set of natural numbers less than or equal to 6. To express: The given set in roster…

Q: Specify the set by roster. {Distinct letters in the word television

A: Given data: {Distinct letters in the word television}   To find: Specify the set by roster.

Q: Define Closed sets ?

A: Closed sets are defined as a set which consists all of their limits points. It is also defined as…

Q: Define two sets, call them A and B, that makes the following statement true; if it is impossible to…

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Q: Explain what is an empty set. Give relevant example along with.

A: Empty set

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Q: Classify the discontinuity of as a removable, jump or infinite?

A: This question is related to continuity and differentiability.

Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

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A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

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Q: Describe the following sets in words and/or pictures: 1. {(x,y,z): y = x2 } 2. {(x,y,z): y > z }…

A: Here, to describe the given sets in words and/or picture.

Q: union of a collectionm of connected sets that have a point in common is conne

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Q: two example of open set in R, closed set in R, and the closure of that set

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Q: Tet X and Y be infinite sets prove that XUY is infinite

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

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Q: Give two evamples that infinite intersection of open Sets not be open. may

A: See the attachment

Q: ☺ Let (u,Ue...,un) be a lineorly ndependent list. Which True Statement? is a has --- a non-zero…

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Q: Prove that derived set of a bounded set is also bounded.

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Q: i) show that a closed interval is a closed set;

A: Note: According to bartleby we have to do only first question please upload the question separately.…

Q: For the universal set U {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y,…

A: Solution:     U – { a, b, c, d, e, f, g, h, i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x , y, z }…

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A: Consider the given set A = {a, b, c}. A proper subset of a set A is a subset of A that is not equal…

Q: If A and B are distinct points in 3-space then |AB| = - Select one: True False

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Q: Prove that the smallest member of a set, if exits, is the greatest lower bound of the set. Correct…

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Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

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Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

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Q: Explain what is an equal and unequal set. Give relevant example along with.

A: Two sets are called to be equal sets when they contains same elements , although order doesn't…

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: I am confused on how to actually find the cardinal number when given an infinite set.Find the…

A: If A is a set with infinite set of natural numbers as A = (x₁, x₂, x₃, x₄…n) where n indicates the…

Q: The defining property of an ordered pair is that two or- dered pairs are equal if and only if their…

A: Firstly suppose that a,b=c,d i.e a,a,b=c,c,d. We have to show that a=c & b=d. There will be two…

Q: Find two examples for equivalet norms on three dimensional real space

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Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

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Q: 4. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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Q: se the roster method to write the set A'.

A: Here use definition of complement of set