For an index set I and indexed families of sets {Ai | i ∈ I } and {Bi | i ∈ I }. For each of the following statements, either prove it or find a counterexample. (∩i∈I Ai ) ∪ (∩i∈I Bi ) = ∩i∈I (Ai ∪ Bi ) (∩i∈I Ai ) ∪ (∩i∈I Bi) ⊆ ∩i∈I (Ai ∪ Bi ) ∪i∈I (Ai ∩ Bi ) = (∪i∈I Ai ) ∩ (∪i∈I Bi )

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Q: D. Let A, B, and C be subsets of some universal set U (a) If ANBC C and A° N B C C, prove that B CC

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A: The given statement is of Baire’s Theorem.

Q: Let A. B and C be sets. In each part, either prove the statement or give a counterexample. (a) AUBCC…

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Q: 1. (a) For a set A, P (A) is the set of subsets of A. Write down all the different elements of the…

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Q: Q1 Let U : Determine the following. {1, 2, 3} be the universal set and let A = (1, 2}, B = (2, 3}…

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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: Prove that if A is transitive set, then A+ is also a transitive set.

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Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

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Q: QLet (X,t) be a topological space and A,E are two subsets of x show that : 3. A is closed set iff A…

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Q: Let A, B be non-empty bounded sets, and A Ç B (A is a proper subset of B). Then sup A < sup B. True…

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Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

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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: Prove that: (i) A is closed. (ii) A = nc. ก ACC closed (iii) A is the smallest closed set in X that…

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A: Let A=1 and B=2.Since, A×B=(a,b)|a∈A, b∈BTherefore, A×B={1,2} -(i)and also, B×A=(b,a)|b∈B,…

Q: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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Q: The empty set o is open set ylgn O İhi O

A: See the detailed solution below.

Q: F oranges pineapples bananas apples pears V peas carrots beans corn potatoes

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Q: Jive R² which are example of two subsets homeomorphic. not C specify the set explicitly) g

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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: Using equality of sets, prove that (?∩?)′ = ?′ ∪?′

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Q: Assume all sets are subsets of a universal set U. Suppose that A, B, and C are arbitrary sets, Prove…

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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: Let U = {x | x is an integer and 0 < 6x < 60} be the universal set that contains the following…

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Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: (b) Let={A i EN} be a family of sets with A₁ CA₂ CCA10 C... Prove that nA = A₁.

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Q: Let U= {1,2,. 1} be the universal set. Let A={x|x eU,x is a multiple of 6, B={x\xeU,xis a multiple…

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Q: A set F is called an Fo-set (or an Fo) if it is a countable union of closed sets. Likewise, a set G…

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