undamental set

Q: List all the subsets of the given set. {g, k, v} Choose the answer that lists all of the subsets of…

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Q: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | x is a…

A: In roster notation, all the elements of a set are listed. In this notation each element is separated…

Q: what is the fuzzy subset ? And give examples

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Q: Prove the absorption law: A ∩(A ∪ B) = A by using either a membership table or definitions and…

A: The given expression is, A∩A∪B=A Proving the expression using a membership table.

Q: Thoorem: is not closed set

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Q: i. PROVE THAT THE EXCLUDED POINT TOPOLOGY ON ANY SET WITH AT LEAST 2 POINTS IS NOT HAUSDORFF. ii.…

A: Definition: A topological space X, τ is said to be Hausdorff if for every x, y∈X there exits U, V∈τ…

Q: i. Provide an example to prove that the arbitrary intersection of open sets is not an open set ii.…

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Q: Proof that : Let A be a finite set with at least 8 elements. Then A can be partitioned into subsets…

A: Given: A is a finite set. and number of elements at-least 8.

Q: cises Using just membership funchion for the following fuzzy sets. (of Course, you must first…

A: The objective is to give a reasonable membership function for the fuzzy sets. a) n is a large…

Q: that apply.) (a)     A = ∅ ∅ {1} {2} {3} {4} {1, 2} {2, 3} {3, 4} {1, 3} {1, 4} {2, 4} {1, 2, 3}…

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Q: 6) Define the cardinality definition of addition.

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Q: Write a set using roster notation the set of the letters in the word indistinguishability

A: According to the given information it is required to write a set using roster notation the set of…

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: Prove or disprove: For all sets A and B, An(AUB)

A: We have to prove or disprove , for all sets A and B A∩(A∪B)=A.

Q: Specify the set by roster.

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Q: Roster form: C = { Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday } What is the Set…

A: To change  roster form to set builder form

Q: If a set is empty then number of subsets

A: Given : Empty set :   It is the unique set which does not contain any element is called as empty set…

Q: True or False: If a set contains ∅ as an element, it cannot be a partition of another set. Please…

A: We know that partition of a set, is a collection of n disjoint subsets, say P1,P2...Pn that…

Q: List all the subsets of the given set {cranberry, orange, fig}

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Q: Roster form: G = {3, 6, 9, 12, 15, 18, 21, …} What is  the Set Builder form?

A: There are 2 ways of representing a set.  Roster form Set Builder form In roster form , all the…

Q: Define Universal set in algebra. State example.

A: Universal set is the set of all elements under consideration in a given discussion. In other words,…

Q: Using properties of sets, show that(i) A ∪ ( A ∩ B ) = A                                (ii) A ∩ ( A…

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Q: Arbitrary unions of closed sets are closed.

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Q: Set is closed

A: To prove that the Cantor Set is closed.

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: True or False?  Every infinite set is unbounded.

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Q: Limikadity malfing ASomozphic Oxdexed sets:-

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

A: Given

Q: The cartesian product of nonempty family of nonempty sets is nonempty صواب ihi

A: The cartesian product of nonempty family of nonempty sets is nonempty

Q: True or False a null set is an element of (-2,-1,1,4)

A: The given set is  (-2,-1,1,4)  Null set is not the element of every set. It is the subset of every…

Q: Bounded Julia (ExH). Why is no Julia Set unbounded?

A: 37)

Q: Using Richard Hammack's book of Elements of Discrete Mathematics chapter 18 in cardinality. Prove…

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Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: Check whether The basis of folowing set not is or 2. 2.

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Q: What is set-builder notation? Give an example.

A: To write: What is set - builder notation. And to give an example of an set - builder notation.

Q: X, Y and Z be subsets of the set . Verify the following properties: XCY XUY=Y⇒XnY=X -UI 3)

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Q: Devise, or create a Set that is Not Well-Defined. Write the set in words. Tell why the set is not…

A: Solution.... A collection of well defined objects or elements is called set.

Q: Prove the empty set hasn't supremum and infimum

A: Lower Bound: A lower bound of a subset A of a partially ordered set (X,⩽) is an element a∈X such…

Q: proof result:  for every two sets A and B, if A-B=B-A, then A-B=null

A: Given A and B are two set such that A-B=B-A for every A and B We have to show that A-B=null that is…

Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

Q: Mathematical Definition: What is a linerarly independent set S?

A: Let S be a non empty set. S = { v1, v2, v3 .... vn}

Q: Question 7.  For any set A, A U A' = {  }

A: Consider the provided statement, “For any set A,

Q: Write a set using roster notation the set of letters in the word indisguishability

A: Concept Used:- In Roster Form All the elements of a set are listed inside curly brackets { } and the…

Q: 2. Let U = {a, b, c, d, e, f, g, h} be the universal set, and let A = {b, c, d, f, g}, B = {a, b,…

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Q: The union of the universal set and any of its subset is * none of the choices cannot be determined…

A: our objective is to conclude

Q: A = {a,b,c} , B ={1,2,3,4}, calculate A cross B. what is the cardinality of the power set of A cross…

A: Given:          A=a,b,cB=1,2,3,4 A×B=a, 1, a, 2, a, 3, a, 4, b, 1, b, 2, b, 3, b, 4, c, 1, c, 2, c,…

Q: rea

A: Let A be set of having n elements, then the total number of subsets of A is 2n. Out of n elements ,…

Q: 0), (1, 0, 0). (3, 2, adependent set

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Q: (a) Using implication table obtain equivalence classes.

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Q: Define bounded set and an example of a set which is bounded below but not bounded above.

A: Bounded set:  A set of real numbers is said to be bounded set if and only if it has an upper and…