Which of the following is true? Select one: O A. A subcover of a cover (E.)aɛI of M is a cover (Sa)acl of M such that Sa C Ea for all a e I. O B. A cover of M is a collection of open sets (E,)act such that M C U E, ael O C. An open cover of M is a collection (E.)act of subsets Ea of M such that U E, is an open subset of M. D. An open cover (E)ael of M is called finite if the index set I is finite.

Q: Prove for all sets of A, B, that P(A) U P(B) is a subset of P(AUB).

A:

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Q: rove the theor

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A: Answer is in following steps.

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A: We used the concept that if a set contains n elements then it power set contains 2n elements .

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Q: Let T be a set such that if the integer x is in T, then 2(x+1) is also in T. Let integer 2 is in T,…

A: Given 2 is in T so 1st and 4th are possible answers.

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A: A ={4, {4},(√4)2}, B={4,{4},{{4}}} A ={3, √(52-32) ,24 mod 7}, B={8 mod 5} A = {{1, 2}, {2, 3}}, B =…

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Q: Which of the following set X has the propert that every subset of X has the first element

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Q: 1. Let A, B, and C be the subsets of U. Then by using laws of sets prove A-(BnC)=(A– B)U(A-C)

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Q: 3. Let A and B be arbitrary sets. Use double inclusion to prove that (A U B) N (A U B') = А.

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Q: 6. Let S be a set with a finite number of elements, and let f: S→→ S be a map (a) If fis onto, can f…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.