Let S be a set of four elements given by S = {A, B, C, D} with the following table. * A B c D A B c A B B c D B A c A B c D D A B D D. Is the binary operation* commutative? Why?

Q: How many distinct 5-letter strings can be created using the letters A, B, C, D, E if repetition is…

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Q: Assume that product codes are formed from the letters V, T, X, R, S, and Y, and consist of 6 not…

A: Available letters  : V, T , X , R , S, Y Repetition is allowed

Q: Draw the Hasse diagram representing the divisibility relation on set A={1,2,3,4,6,12,24}. ·…

A: A=1,2,3,4,5,6,7,8,9,10 = (1,1) (1,0) (1,3) (1,4) (1,6) (1,12) (1,24) (2,2) (2,4) (2,6) (2,12) (2,24)…

Q: Write in Roster form: Set of all Dean’s lister in a university

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Q: A combination is a selectio objects from а. n objects

A: Combination is a technique which represents the number of possible outcomes from n objects

Q: Let U = { 14, 15, 16, 17, 18, 19, 20 }, A = { 14, 16, 18, 20 }. Use the roster method to write the…

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Q: Suppose we have 15 graphics cards and 4 servers. The graphics cards are all identical, but…

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Q: Assume that product codes are formed from the letters A, B, C, D, and E, and consist of 5 not…

A: Product code is formed by the letters A, B, C, D, and E and consists of 5 not necessarily distinct…

Q: Give the transpose of the permutation [2, 5, 1, 6, 3, 4], and find the number of inversions in both…

A: To find- Give the transpose of the permutation 2, 5, 1, 6, 3, 4, and find the number of inversions…

Q: Use inclusion-exclusion to find the number of ways to arrange the six numbers 1, 2, 3, 4, 5, 6 such…

A: please see the next step for solution

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: Assume that product codes are formed from the letters Q, X, W, T, S, Z, and Y, and consist of 6 not…

A: 1) There are total 7 letters, such that, Q, X, W, T, S, Z and Y.

Q: Let's suppose that a password must contain 4 characters, where a character can be any of the digits…

A: Total number of digits = 5 Total number of letters = 26 Total options are 5 numbers + 26 letters =…

Q: 2. Let, a, = 3, az = 4 and for n 2 3, a, = 2a,-1 + an-2+ 5, express a, in terms of n.

A: Topic:- series sum

Q: Suppose A₁, A2, ..., A30 are thirty sets each having 5 elements and B₁, B₂, ..., B₁ are n sets each…

A: Given that A1, A2, . . ., A30 are thirty sets each having 5 elements and B1, B2, . . ., Bn  are 'n'…

Q: Suppose B is a set containing two distinct element called 0 and 1: suppose there are defined on B…

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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: Consider selecting two elements, a and b, from the set A = {a, b, c, d, e}. List all possible…

A: All possible subsets having 2 elements of given set A ={a,b,c,d,e}  Are given below

Q: Assume that A={A,B,C} and B={5,4,1,9,6} A code consists of 2 different symbols selected from X…

A: Given: Assuming X={A,B,C} and Y={5,4,1,9,6}. A code consists of 2 different symbols selected from X…

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: How many strings of seven lower case letters of the English alphabet contain exactly four letters w…

A: We have to use permutations and combinations here.

Q: Assume that X={G,E,D,A}X={G,E,D,A} and Y={5,6,1,2,7}Y={5,6,1,2,7}. A code consists of 2 different…

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Q: Let [A1, A2. [B1, B2, C1, C2 be 3 married couples who attended a concert in Windhoek. a) In how many…

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Q: 1. How many words of length 5 are there on the set {A, B,C, D} which do NOT contain the string…

A: As per our honor code, we are authorized to answer only one question at a moment. As you have not…

Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

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Q: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: so the S and T remain next to each other (though not necessarily in that order, so ST or TS are both…

A: Consider as S and T as one letter. So now the total number of English alphabet which needed to…

Q: Let A = ,2,3,45,6,73 How many subsets ot Contriin d) How many anly even numbers? subsets. ot A…

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Q: Let E be the set of 26 English letters. Find the number of 5-letter words (including  nonsensical…

A: There are totally 26 English letters in which 5 are vowels(A, E, I, O, U) and remaining 21 are…

Q: A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work…

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

A: A detailed solution is given below.

Q: Is A a subset of B if A = {2, 3, 5, 7, 8, 9, 10} andB = {3, 5, 8, 9}?

A: The given sets are, A=2,3,5,7,8,9,10B=3,5,8,9 A set A can be said to be the subset of another set B…

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

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

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Q: Let U = 51, 2, 3, 4, 5, 6, 76, A = 51, 3, 5, 76, and B = 53, 4, 66. Find each set. U^{\prime}

A: Given sets - U = 51, 2, 3, 4, 5, 6, 76A = 51, 3, 5, 76B = 53, 4, 66We need to find the prime or…

Q: Let A denote the set of all 4 digit numbers that are divisible by 3, and B denote the set of all 4…

A:

Q: 2. Let S be the set of three elements given by S = {A, B, C} with the following table. * A B A A B B…

A: From the given table , we can see that  A*B=B= B*AA*C=C=C*AB*C=A=C*B So, the binary operation * is…

Q: Suppose we have 5 alphabets (a, b, c, d, e) and 5 envelops (?1,?2,?3,?4,?5)   In how many ways we…

A: Suppose we have 5 alphabets (a, b, c, d, e) and 5 envelops (?1,?2,?3,?4,?5)   In how many ways we…

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

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Q: Assume that product codes are formed from the letters V, T, X, R, S, and Y, and consist of 6 not…

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Q: 5 can be formed if the alphabet (set of avail

A: To find: Number of strings of length 5 that can be formed with {a,b,c} with last character not as b.

Q: License plates in China begin with a Chinese character designating the province, followed by a…

A: We have 1 character for the Chinese Province which we won't consider as we want only for the case of…

Q: Let A denote the set of all 4 digit numbers that are divisible by 3, and B denote the set of all 4…

A: Given, A denotes the set of all 4 digit numbers that are divisible by 3 B denote the set of all 4…

Q: A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work…

A:

Q: The greetest common divisor of two number 1, b(nteger) are None of the mentioned 6+1

A: To find greatest common divisor of two numbers 1 and b(integer)

Q: 9. Jse set builder notation to express the set (1, 4, 7, ..., 298, 301).

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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: How many permutations of the 26 letters (English alphabet) do not contain any of the strings zero,…

A: Total number of permutations of 26 letters  (N) = 26! Number of permutations in which ZERO always…

Q: How many length-4 lists can be made from the symbols A, B, C, D, E that contains at least one letter…

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Q: Assume that A = { 1, 3, 5, 8, 9}and that U = set of natural numbers less than 11. Find A'. * O {2,…

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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”.