let X={a,b,c} Construct two topologies for the set that have at least 4 open and that are equivalent (and show why they are)

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: Find an orthogonal set with the same span (and same number of elements) as 7 -5 4 4 7 (198) -10 -8…

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Q: Give an example of a set with a finite number of points that is not se-quentially compact, or else…

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Q: If finite set A has a elements and finite set B has b elements, and a> b what is the minimum number…

A: Given that set A has a elements,  n(A)=a and set B has b elements,  n(B)=b with a>b .We have to…

Q: If AnB is pathwise connected set.  then A and B are:  a. Pathwise connected sets b. Not pathwise…

A: Pathwise connected means any two points in that set can be join by a continuous function. Roughly…

Q: I don't understand why you put Ui element of I. I think you made a mistake. Please let me know.…

A: Step 1:Step 2:Step 3:Step 4:

Q: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

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Q: For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅. Let the universal set U be {1,…

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Q: True or false? A∩(B∪C)=(A∩B)∪(A∩C) You should determine this by building the Venn Diagram for each…

A: Given statement is A∩(B∪C)=(A∩B)∪(A∩C)

Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

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Q: Is the set S linearly independent? b.  Is v = (1, -2, 1) in the span of S?   If not, show why not.…

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Q: 2. Let X= [0, 10] be the universal set and A = [1,4], B = (2,8), C = [3, 6) be the subsets of X.…

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Q: You are given two sets such that a set is not a subset of other. If you have to prove this,how do…

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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: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

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Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

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Q: Let A and B be subsets of some universal set U. Prove each of the following: *(a) An BCA * (b) A…

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Q: Consider the set, S = {(5, 0, 3), (10, 0, 7), (0, 5, 0)} Answer the following questions. Your work…

A: Given set is s={(5,0,3),(10,0,7),(0,5,0)} we have to find  a) if s is linearly independent? b) does…

Q: Could the explanation of how each cardinality set is determined be described?

A: Cardinality :  It is the number of elements in a mathematical set. In question there are three…

Q: Find an example of a set A with |A| = 3 which contains only other sets and has the following…

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Q: Set U is the set of farms in a certain country. Set A is the set of farms in the country that…

A: Given that , U = Set of farms in a certain country A = Set of farms in the country that produce corn…

Q: Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A…

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Q: Let A and B be infinite sets that are uncountable. Do an and B have the same car finality as each…

A: Let A and B be infinite sets that are uncountable. Do A and B have the same cardinality as each…

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

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: Determine whether the following statements are true or false: (a) The empty set ∅ is a subset of {1,…

A: Empty set is a subset of every set. A Power Set is a set of all the subsets of a set.

Q: X, Y and Z be subsets of the set . Verify the following properties: XCY XUY=Y⇒XnY=X -UI 3)

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Q: Denote the set in set-builder form {6, 12, 18, ….66}

A: The objective is to denote the set {6, 12, 18, ….66} in set-builder form.

Q: Show The union of a finite number of open sets in R is an open set.

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Q: (FNB) UC'

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Q: How to Apply the Archimedes'principle to prove that a set is empty

A: Consider the given information. the Archimedes' principle is defined as, Property states that for…