Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of thefollowing may be considered as universal set (s) for all the three sets A, B and C(i) {0, 1, 2, 3, 4, 5, 6}(ii) {0,1,2,3,4,5,6,7,8,9,10}(iii) {1,2,3,4,5,6,7,8}

Q: How many subsets of the set {1,2,3,4,5,6,7,8} have cardinality 3 or less?

A: Here we need to find how many subsets of the set A={1, 2,3,4,5,6,7,8} have cardinality 3 or less so…

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: 5. (a) Let A ={1,2,3,4,5} and B = {2,3,4}. How many sets C' have the property that C C A and BC C…

A: (a) The given set A is as follows. A=1,2,3,4,5 The subsets of A such that B is a subset of it is as…

Q: What is the domain of the following {(3, 4), (9, 1), (10, 5), (2, 15), (8, 4)} O {3, 4, 9, 1, 10, 5,…

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Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: Example 5. If A, B and C are three sets and U is the universal set such that n(U) = 1000, n(A) =…

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Q: Is the set S linearly independent? b.  Is v = (1, -2, 1) in the span of S?   If not, show why not.…

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Q: 2. Let X= [0, 10] be the universal set and A = [1,4], B = (2,8), C = [3, 6) be the subsets of X.…

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Q: What is the domain of the following: {(3,4), (9,1), (10, 5), (2, 15), (8,4)} O {3,4,9, 1, 10, 5, 2,…

A: Domain of a function: The domain of a function fx is the set of all values of x for which the…

Q: If a universal set contains 250 elements,

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Q: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

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Q: List the first four elements in order of the set { x | x = 4k + 1, and k is a natural number} (List…

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Q: A universal set U with 156 elements has been partitioned into three subsets, A, B, and C. If B is 5…

A:

Q: Consider the set, S = {(5, 0, 3), (10, 0, 7), (0, 5, 0)} Answer the following questions. Your work…

A: Given set is s={(5,0,3),(10,0,7),(0,5,0)} we have to find  a) if s is linearly independent? b) does…

Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

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Q: 12. List all possible subsets of the set {2,, d}

A: Given set : { 2 , π , d }

Q: Are the sets A_4 and A_5 compact sets? Why yes, why not? Ay = (,2] A- [1, 2] u [ 3, +]

A: See the attachment

Q: What is the cardinality of the power set of a set with 4 elements?

A: Introduction: The cardinality of a set:The cardinality of a set is the total number of unique…

Q: Let S = {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows,…

A: We want to find nA∪B'

Q: Let the Universal set be U = (1, 2, . 20), A= (1,6.11,19) and B = (6, 11, 14, 7) f(A - B) (1) = (A5…

A: Since you have posted multiple questions. I am answering the three parts. Please post the question…

Q: What is (A∪B)c where A={5,11,3,8,9} , B={99,5,11,2,4} and Universal Set…

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Q: What is the cardinality of the power set of a set with 5 elements?

A: The power set of a set S, denoted by P(S), is the set of all possible subsets of S, including the…

Q: What is the domain of the following: {(3,4), (9,1), (10, 5), (2, 15), (8, 4)}

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Q: Answer the following True or False. (a) {1,2,3} is a subset of {3,2, 1, 4). (b) (3,2, 1,4) is a…

A: We have to find given statements are true or false.

Q: What is the domain of the following: {(3,4), (9, 1), (10, 5), (2, 15), (8, 4)} O {3, 4,9, 1, 10, 5,…

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Q: How many subsets of a set with 64 elements have more than two elements

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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: If X = {u,v} what is the power set of X? (in answering this question, use {} as the null set, and do…

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Q: 4. Find all subsets of S = {0, 1, {0,1}} which are not also elements of S. (Another way of writing…

A: 4. Given set is S=∅, 1, ∅, 1.   To Find: All subsets of S which are not also elements of S i.e., all…

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…

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”.