How many elements are in A ∩ B  U= {1,2,3,4,5,6,7} A={1,2,4,5} B={1,3,5,7

Q: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9}. Find A′.

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Q: 4. How many subsets are there of {1, 2, 3, 4, 5}? How many contain at least three elements? How many…

A: Given set is S=1,2,3,4,5 Since we know that, if a set contains n elements, then total number of…

Q: Let A, = [0, 2 + ±], for n = 1, 2, 3, 4, 5, . .. Find n U An and ( An ? n=1 n=1

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Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Given information- We have given that the set S has 7 elements. We have to find the number of subset…

Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

Q: How many proper subsets does the set W, containing the days of the week, have? W={Monday, Tuesday,…

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Q: Let A = { a, e, i, o, u} and B = { a, b, c, d}. Is A a subset of B ? No.(Why?). Is B a subset of A?…

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Q: Given that U = {1,2, 3, .., 11, 12, 13} A = {3, 5, 8, 9, 13} B= {3,5, 6, 8, 9, 10, 11, 12} C = {4,5,…

A: As per our company guidelines we are supposed to answer only first 3 subparts. Kindly repost other…

Q: Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8} and E = (0, 2, 4, 6, 8} and P = {2, 3, 5, 7}, then the…

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Q: 16. How many 6-element subsets of A = {0,1,2,3,4,5,6,7,8,9} have exactly three even

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Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

Q: 1. Let A, B and C be members of C. Compare An(BuC) and (A

A: Suppose there are two sets A and B then, the union (∪) of these two sets is defined as a set…

Q: How many sets of are in 2-½?

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Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: How many subsets of S do not contain any upper case letters?

A: given set S=A,B,a,b,c,d,1,2,3,4 claim- to find how many subsets of Sdo not contain any upper case…

Q: In how many ways can we compose a word of 3 letters from the set {X, Y, Z, F, S} if repetition is…

A: Given, Letter set  = {X, Y, Z, F, S}  words should be 3 letters,

Q: 2. Let S be a subset of {1,2,. 99} with exactly 10 elements. Show that S has two disjoint subsets…

A: Given: S=1,2,....99 Number of subsets with 10 elements 210=1024 Maximum sum of 10 elements from…

Q: 2. How many 3 element subsets of the set {a, b, c, d, e, f, g, h, i} contain no vowels?

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Q: A(n) _____ is a collection of items called elements

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Q: 6. Show that for n attributes A, A2, A3, ..., An (A, Az Az ... A, ) > ( A, ) + ( A2 )-(A3) + ... + (…

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Q: Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and    B = {3, 4, 5}. Find A′, B′ , A′ ∩ B′, A ∪ B and hence…

A: Given: Now, The set of all those elements of U which do not belongs to A is called the complement…

Q: A1,...,A13 are thirteen different subsets of {1,2,3,4,5,6,7,8,9,10}. If each Aj has 6 elements for…

A: We are given that A1, ... , A13 are thirteen different subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.…

Q: If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A={1, 3, 4, 6, 9} and B = {3, 6, 7, 9}, list the elements of the…

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Q: If A=(1,2,3,4,5.6,7), What is the number of nonempty subsets of A?

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Q: Number theory

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Q: Let A = {1, 2, 3, 4, 5}. How many subsets of A have no more than 3 elements?

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Q: Find the number of distinguishable permutations of the group of letters. Z, V, C, C, V, C, C, V, M,…

A: Letter   Frequency---------  ----------Z                1V                4C                4M…

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Consider that  the set S has 7 elements. The subsets can have 3 elements, 2 elements, 1 element, and…

Q: Let U = {1,2,3,4,5,6,7,8,9,10} and A = {1,3,5,7,9). Find A". ....

A: Given, U=1,2,3,4,5,6,7,8,9,10   AndA=1,3,5,7,9

Q: Let A {1,3,5, ... }, then A is well- ordered.

A: Here we have given a set A ={1,3,5,  ...}

Q: Find the number of distinguishable permutations of: 6 Ds, 5 Js, and 2 Os

A: our objective is to find the no. of permutations

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and    B = { 2, 3, 5, 7 }. Find A ∩ B and hence show that A…

A: A ∩ B = {1,2,3,4,5,6,7,8,9,10} ∩ {2,3,5,7}           = {2,3,5,7}           = B

Q: 2. Among 500 graduating students, 210 of them smoke, 258 drink alcoholic beverages, 216 eat between…

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Q: 17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400…

A: Here, n(A)= 100, n(B), 150, n(C)=250, n(D)=400 n(A∩B)=15, n(A∩C)=15, n(A∩D)=15, n(B∩C)=15,…

Q: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; wheren is total number of distinct…

A: Consider two sets A and B. Then the union of these two sets contain all the elements in both A and…

Q: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

A: A proper subset of a set A is a subset of A that is not equal to A.Or in other words, if B is a…

Q: If a,,a,, a3,., a, are in HP, Prove that a,a, +a,a; +...+ a,.1 a, = (n - 1)a,a,.

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Q: Let S := {l, a, t, e, r, a, l}. How many subsets does S have?

A: Given: S = {l, a, t, e, r, a, l} Here, number of elements is n = 7.

Q: 15 Assume that set S has 11 elements. How many subsets of S have at most 2 elements?

A: Solution : A set S has 11 elements We want to find subset of S have at most 2 elements

Q: Let A = {small, medium, large}, B = {yellow, orange}, and C = {triangle, round}. List the elements…

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Q: 1. Find the number of permutations of the elements in the set 1,3,5,7,9,11. 2. How many different…

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Q: Let D be a standard deck of cards, let SV = {A♡, K♡,Q♡, JO}. a) List all the subsets of S♡ that…

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Q: Let U= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 3, 4, 5, 6}, and B = {0, 3, 6, 9}. Find A NB.

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Q: Let A = {a,b, c} and B = {b, c, a}. Prove that A = B. Thus, the order %3| in which the elements are…

A: The given sets are A={a,b,c} and B={b,c,a}we have to show that A=BResult : two sets A and B are…

Q: Show that for n attributes A1, A2, A3, ..., A, (Aj A2 Az ... A, ) 2( Aj ) + ( A2 ) + ( A3 ) + ... +…

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Q: How many possible unique deck orders can w • 1, 2, 3, 4, 5, 6, 7 to • 2, 6, 1, 7, 4, 3, 5 O 3 O 9 10…

A: Given numbers: 1, 2, 3, 4, 5, 6, 7.

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В 3D {3, 1, 9, e, а, с, 0}, and С %3D {2, с, 10, 9, 8, —4,…

A: Using the definition of intersection, union and difference between two set

Q: Let S = {a, b,f,g, i, k, m, q, t} . (1) How many subset of S have exactly 3 elements? (2) How many…

A: We have to find no. Of subset as per given question.

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”.