Define Open set ?

Q: What is set-builder notation?

A: Definition of set-builder notation:

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

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: What is a set?

A: Definition of the set:

Q: Express the set in set-builder notation {24, 32, 40, 48,....,88}

A: Consider the given set. Rewrite the elements of sets as the multiple for 8. Given set=24, 32, 40,…

Q: Which set has higher cardinality: N or Z? Explain with example

A: Cardinality: The cardinality of a set A is the number of elements present in the set A. We denote…

Q: The set of elements that are members of set A or set B or of both sets is called the --------------…

A: The union of two sets is composed of elements of the same two sets.

Q: Explain the main difference between Julia set and a Mandelbrot set.

A: We know that, For a complex numbers c, Both Julia set and Mandelbrot set of c is the set of all z…

Q: The set of elements common to both set A and set B is called ----------------- the of sets A and B,…

A: Sets are basically a collection of well defined and distinct objects. These objects can be anything,…

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

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Q: Express the set using the roster method. the set of natural numbers less than or equal to 6.

A: Given: the set of natural numbers less than or equal to 6. To express: The given set in roster…

Q: What is a set? What is a subset? How can we show that a set is equal to another set, using this…

A: To define: the set, subset. To show: a set is equal to another set. Please post the multiple…

Q: Write out in words the description of the set. {x\x € W, x < 9} The set of ---Select--- X, such that…

A: To write out in words the description of the set.

Q: Use the roster method to list the elements in the set: {x|x is a whole number less than 4}.

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Q: Define two sets, call them A and B, that makes the following statement true; if it is impossible to…

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Q: Explain what is an empty set. Give relevant example along with.

A: Empty set

Q: Explain what is a finite set. Give relevant example along with.

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Q: why Ua equals to empty set

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Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

A: A set is said to be convex if for any two points in the set the line segment joining those points is…

Q: define sets.

A: A set is a collection of well defined objects.

Q: Give an example of a bounded set that has infinitely many isolated points

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Q: Determine if the union/intersection of two open sets is always open then determine if the…

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Q: subset

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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: What is meant by Union of sets?

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Q: Give an example of a countable collection of bounded sets whose union bounded, and an example where…

A: Let A1 and A2  are bounded sets

Q: The empty set is open set

A: See the detailed solution below.

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: What are the basics of a set?

A: Set:A set is a collection of well-defined distinct objects. Here the objects are known as the…

Q: Define a set of which both {1, 3, 4} and {0, 3, 5} are subsets. Find such a set with the smallest…

A: {0,1,3,4,5} is the smallest set that contains {1, 3, 4} and {0, 3, 5} as sub-sets.

Q: Identify the set shown below as finite or infinite, {10, 11, 12, ..., 40} ..... OInfinite O Finite

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Q: i) show that a closed interval is a closed set;

A: Note: According to bartleby we have to do only first question please upload the question separately.…

Q: determine the number of subsets of a set with 21 elements

A: To determine the number of subsets of a set with 21 elements

Q: Prove that empty set is subset of all sets: φ ⊆ A     Please help me figure this question out.

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Q: Write an example of a partially ordered set which is not totally ordered. Explain the reasons. Are…

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Q: Give a set that is not closed under addition

A: In the question we have to give a set that is not closed under addition.

Q: 5. Show that a finite set is a closed set.

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Q: Let U be the universal set of all the letters in the English alphabet. What is the complement of the…

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Q: Prove that the greatest member of a set, if exits, is the least upper bound of the set,

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Q: specify the set by roster distinct letters in the word (mathematics)

A: Given that

Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

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Q: ) Find an example of an infinite collection of closed sets whose union is not closed.

A: Any closed interval is closed in R. From that we created this example.

Q: Explain what is an equal and unequal set. Give relevant example along with.

A: Two sets are called to be equal sets when they contains same elements , although order doesn't…

Q: undamental set

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Q: 2. Write the set of positive odd integers in set-builder notation.

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Q: show vacuous proof of statement that "empty set is a subset of any set"

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Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

Q: Give example closed set and bounded set is compact

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Q: se the roster method to write the set A'.

A: Here use definition of complement of set