. II is the set of even integers. Which set is a proper subset of I? a,{}{} b{−3,−1} c{2,3,4} d{25,27,29,…} 2.If X={…,1,2,3}, then which set is a proper subset of X? a{0,1,2,…} b{−8,−10,−13 c{2,3,4} d{…,1,2,3}

Q: 7. i) How many functions are there from the set {1, 2, 3, ...,k} where k is a positive integer, to…

A:

Q: For the set ?={−3,0,57,−8‾√,2.314520968724609....,14}A={−3,0,57,−8,2.314520968724609....,14}.…

A: Given :A=-3,0,57,-8,2.314520968724609...,14To indentify those that are…

Q: 1. Let A = {2, {2},{{2}}}, B = {2, {2}, {2, {2}}}. Is A C B? Is BC A? Is either A or B a proner…

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Q: How would you write a formal proof for if AnB = B then B is a subset of A?

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Q: a. Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and…

A: # we are entitled to solve one question at a time. Please resubmit the other questions of you wish…

Q: 7. If any subset of size five is chosen from {1, -1, 2, -2, 3, -3, 6, -6}, then prove that each of…

A: Given: Sample space={1,-1,2,-2,3,-3,6,-6} Subset of size 5 is chosen from sample space.

Q: 5.The sum of 100 real numbers in a given set X equals zero. Prove that the sums of at least 99 pairs…

A: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is…

Q: Z+ is the set of positive integers. Let A = {1,2,3), B = {n ∈ Z+ | n is even}, C = {n ∈ Z+ | n is…

A: concept Used: C∩D is the set  containing all elements of C that also in the set D C∪D is the set…

Q: 4. Is the set Q² x {a,b,c} countable or uncountable? You must justify your answer with a proof.

A: Given : ℚ2×a , b ,c  To Prove : ℚ2×a , b ,c  countable or uncountable

Q: Find the number of elements of the set {n/n € Z,1 <n < 1000, 2 {n and 3 {n and 5 fn and 7 {n}.

A: By using set theoretic rules you can solve the given problem as follows :

Q: Which of the following statements is correct about the set -3 6 -898) 2 -4 -2 S = Select one: O O O…

A: There is set S given. One has to check whether S spans the vector 333 and vector space R3 or not.…

Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

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: Determine the identity element of the set N={1,2,3,..} of positive integers with addition.

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Q: Which of the following pairs of sets is a disjoint set? O (1,2,3,4) and (x x is a natural number and…

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Q: Let A2A2 be the set of all multiples of 2 except for 2.2. Let A3A3 be the set of all multiples of 3…

A: Let A and B be two sets. Then the union of two sets will be the set that will contain all the…

Q: What can you say about the sets A and B if AB=A?

A: Consider two sets A  and B. Then the symmetric difference between these two sets is denoted by A⊕B.…

Q: 11. a. Is 3 € {1,2,3}? d. Is {3} € {1,{2}, {3}}? e. Is 1 € {1}? h. Is {2} € {{1},2}? į. Is {1} =…

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Q: How many relations are there on the set S = {2, 4, 6}?

A: We know that, the number of relations of a set containing n element is 2n^2. Given that S = {2,4,6}

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Let U = {x | x is an integer and 0 < 6x < 60} be the universal set that contains the following…

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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: Which of the following could be considered as NOT an equal set? B = (x : xe Z, -3 < x 0}; C = {0,…

A: Equal sets are the two sets having same element.

Q: 2. Let A = {1, 2, 3, 4, 5, 6} and B= {2, 4, 6, 8}. What is the cardinality of B? A U B, A N B?

A: Given that  A={1, 2,3,4,5,6} and B={2, 4,6,8}

Q: 2. (Sets) Given the universal set U= {n € N |1SnS 10), and the sets A= {n €U |n is the square of an…

A: U=n∈ℕ| 1≤n≤10 List of all universal set U=1,2,3,4,5,6,7,8,9,10

Q: I. Let the universal set U {1,2, 3, ..., 10} . Let A = {1,4, 7, 10}, B= {1,2, 3, 4, 5}, and C = {2,…

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Q: Prove that a selection of 7 numbers from the set {1, 2, . . . , 11} contains numbers m and n such…

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Q: 12. A real number x is called algebraic if there is a positive integer n and integers aŋ, a1, 7 0.…

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Q: 3. (GYHD 5) Write each of these statements using "V": a) S is closed under addition. (Here, S is a…

A: (a). Given that S is closed under addition. (Here, S is a subset of ℤ.)

Q: Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. [Note:…

A: Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. [Note:…

Q: Find the union or intersection as indicated for the given sets. A = {x | x ∈ the natural numbers…

A: What is Sets: Simply put, a set in mathematics is a grouping of different items. Any group of…

Q: ers are a subset of vegetables. D. Birds are a subset of mammals. 3. If the universal set is the set…

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Q: Let a, be the set {0, 2, 12} Let a, be the set {4,5, 10} Let az be the set {6,9, 14} Let az be the…

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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”.