Give a set that is not closed under addition

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: Define Open set ?

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Q: Cavity Candies mass produces an assortment of hard candies, consisting of three flavors: cinnamon,…

A: Solution:

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: list all the subsets of  {1,2,∅}   and {{R}} R= real number

A: Number of subsets of a set with n elements is 2^n

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

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Q: why Ua equals to empty set

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Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

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

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Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

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

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Q: Prove. Power set of a null set is empty.

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Q: Prove that an enumerable set is infinite.

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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: open

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

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Q: *· Given a set (x, x+3, x+6, x+9, x+12} where xE2*, show there exists at minimum 1 of the numbers in…

A: Given set is x,x+3,x+6,x+9,x+12 where x∈ℤ+ The objective is to show that there exists at minimum 1…

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

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: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

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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…

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”.