A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2 times the size of A and C is 4 times the size of B, then how many elements are in B?

Q: How many unordered selections of three elements can be made from the set {a, b, c, d, e, f}?

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Q: List all the subsets of the set                   { –1, 0, 1 }.

A: All subsets of {-1,0,1} is:

Q: If a given set has 15 elements how many of its subset have at most two elements

A: Given, No of elements=15  how many of its subset have at most two elements

Q: (a) In how many can the set {1; 2; ........; 16} be partitioned such that each part contains 2…

A: (a) Definition : Partition problem is to determine whether a given set can be partitioned into two…

Q: 20

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Q: Set A contains 19 elements, set B contains 22 elements, and 6 elements are common to sets A and B.…

A: A set is a well-defined collection of objects, these objects are called the elements of the sets.…

Q: Consider a bag containing five red marbles, two green ones, one transparent one, five yellow ones,…

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Q: Write out the indicated sets by listing their elements between braces

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Q: If set Z has 7 elements, how many subsets does it have?

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Q: Consider a bag containing four red marbles, three green ones, one transparent one, three yellow…

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Q: How many subsets with an odd number of elements does a set with 12 elements have?

A: Given that a set contains 12 elements. We need to calculate the total number of subset with an odd…

Q: Assume that the candle manufacturer has 7 types of round candles and 5 types of square candles…

A: Permutations and combinations: When one has to choose among a set of objects or people, then…

Q: Find the number of subsets that can be formed from a set containing 10 elements.

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Q: Consider a bag containing four red marbles, three green ones, one transparent one, three yellow…

A: Given, four red marbles,three green ones, one transparent one, three yellow ones, and three orange…

Q: If A and B are both finite sets and A has n elements and B has m elements, what’s the fewest number…

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Q: Given that set A has 41 elements and set B has 22 elements, determine each of the following. (a) The…

A: Set A : 41 elements  Set B : 22 elements

Q: 6.3.16 How many subsets with an odd number of elements does a set with 10 elements have?

A: Consider that the set has 10 elements and we need to find the subsets with an odd number of…

Q: Calculate the number of subsets and the number of proper subsets for the given set. {x|x€N and…

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Q: How many unordered sets are possible that contain three objects chosen from seven?

A: Number of unordered sets that contain three objects chosen from seven = 7C3

Q: How many unordered sets are there of two items chosen from four? sets

A: To Find: How many unordered sets are there of two items chosen from four? Concept: Crn=n!r!n-r!

Q: If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A…

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Q: How many subsets with an odd number of elements does a set with 10 elements have?

A: To find the total number of subsets with an odd number of elements of a set with 10 elements, first…

Q: Suppose A is a set with 6 elements. Answer the following questions:   1. How many subsets of…

A: In a set the order does not matter. So we can use the combination method. 1) We can pick 4 elements…

Q: Show that if any 14 numbers are selected from the set S = {1,2, 3, ..., 25}, %3D there are at least…

A: Given statement is If any 14 numbers are selected from the set S = {1,2,3,...,25}, there are at…

Q: If A is set of all vowels in alphabets.Then number of subsets of A is

A: Given: A contains all vowels  So, A = a, e, i , o , u Number of elements in A = 5

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

A: There are 10 digits as 0,1,2,3,4,5,6,7,8,9 and 26 letters, which are “ a, b, c, d, e, f, g, h, i, j,…

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

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Q: Consider a bag containing four red marbles, three green ones, one transparent one, four yellow ones,…

A: Given:  4 Red Marbles 3 Green Marbles 1 Transparent Marbles 4 Yellow Marble 3 Orange Marble  To…

Q: A universal set U with 48 elements has been partitioned into three subsets, A, B, and C. If B is 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 many subsets is obtained from a set with 5 elements?

A: Given n=5

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: 3. Find the number of subsets for set containing 3 elements.

A: Given set  containing 3 element

Q: Suppose that set A has 17 elements, set B has 10 elements, and their union has 18 elements. If the…

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Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: How many unordered sets are there of five items chosen from eight?

A: In unordered sets, the order of the selection of the selection of items does not matter. So,…

Q: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

A: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

Q: Given a set has m members, where m=15, how many proper subsets are there?

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Q: if a given set has 24 elements how many of its subsets have at most four elements

A: There are subsets with 0 elements, 1 element, 2 elements, 3 elements, and 4 elements which are…

Q: Draw a diagram out of these sets

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Q: Show that if A is a countable set, and B CA is infinite, then B is countable. [Hint: How could we…

A: To prove that  If A is a countable set and B is a subset or equals to A is infinite then B is…

Q: b) The number of elements of the set A = {{{Ø}}, {{Ø}} n {Ø}, {Ø} U {Ø, {Ø}}} equals

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Q: Suppose we have four sets with sizes 50, 60, 70 and 80. Each pair of sets has five common elements…

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Q: Suppose A is a set with 7 elements. Answer the following questions: 1. How many subsets of exactly…

A: Given, A is a set with 7 elements In a set the order doesnot matter so here we use combinations.

Q: Suppose XX is a set with 144 elements that is partitioned into four subsets: X1, X2, X3, and X4. If…

A: To determine the number of elements in each subset in the partition.

Q: How many subsets of a set with 50 elements have more than one element?

A: Introduction:  Here we need to find how number of subsets have more than 1 element. Given:…

Q: Consider a bag containing seven red marbles, two green ones, one transparent one, seven yellow ones,…

A: Determine the number of sets of five marbles include at most one of the red ones but no yellow ones.…

Q: (1point) How many elements are in the union of four sets if each of the sets has 99 elements, each…

A: To find: The number of elements are in the union of four sets if each of the sets has 99 elements,…