For each condition below, give an example of a set that satisfies that condition, or prove that one does not exits (a) An open set that is a subset of Q (b) A non-empty open set that is a subset of Q (c) A non-empty closed set that is a subset of Q (d) Two disjoints open sets whose union is R (e) Two non-empty disjoints open sets whose union is R (f) An infinite subset of R with no limit points. (g) A bounded infinite subset of R with no limit points. (h) An infinite union of closed sets that is not closed.

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: Give an example of a set that satisfies the condition, or prove that one does not exist: An…

A: The statement or condition :An infinite intersection of non-empty closed sets that is empty.

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: Provide a counter example that infinity intersection of open set is open

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Q: True or False The intersection of two sets is always a subsetof their union

A: To check the statement

Q: Define E to be the empty set and further define F = {E}, G = {F}, H = {E, F}, and I = {E, F, G,H}.…

A:

Q: C = {whole numbers} and D = %3D {rational numbers} A={multiples of two} and B = {multiples of three}…

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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: Prove that (2,5) is an open set

A:

Q: (a) Let A, B be sets. Prove that A\(An B) = A\B. You may assume all sets in the question are…

A:

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: Suppose that the universal set for all variables is Z, and let P(a, b, c) be the predicate a^2 = |b…

A: Given: The universal set for all variables is ℤ. Pa, b, c is a predicate a2=b-c. To provide:  (a) an…

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

A:

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: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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

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

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Q: Let the domain be the set of all people. Let: P(x,y): x knows y. Which of the following is the…

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Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

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Q: Consider two sets A and B such that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find the set C…

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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…

Q: Use the set definitions A = {a, b} and B = {b, c} to express the elements in the powerset P(A) ∩…

A:

Q: TRUE (c) The union of two sets, A and B, is the set of all elements in A and B. FALSE

A: We have to say whether it is true or not " The union of two sets A and B is the set of all elements…

Q: Use graph to find set. [2, ∞)∩ (4, ∞)

A: Use the graph to find [2,∞)∩(4,∞)

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

A:

Q: Find the closure of each of the following sets: mod T d (a) (3,5) U {6} (b) (-∞, 0) U (0, 1)

A: Given: (a) 3, 5∪6     b -∞, 0∪0, 1 To find: Closure of the given set.

Q: The number of relations on the set A = {1, 2} is 256 . O True False

A: Number of relation with n elements 2n2

Q: Give an example of an infinite collection of open sets whose intersection is not open.

A: Here, we have to give an example of an infinite collection of open sets whose intersection is not…