Let ? and ? be permutations on the set {1,2,3,4,5,6,78,9}, defined as follows

Q: a) Let S={a, b, c}, and for each integer i= 0, 1, 2, 3, let S, be the set of all subsets of S that…

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Q: If A is a perfect subset of B and P(a < Pb), then P(BA) is equal to O a. P(a) / P (b)

A: Given: A is a perfect subset of BP(a &lt; Pb)

Q: How many distinct permutations can be formed using all the letters of the word MATHEMATICS? 11!…

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Q: Let U = {3, 4, 5, 6, 7, 8, 9, 10},  A = {4, 6, 8},  B = {3, 4, 7, 10}, and C = {3, 5, 7} . Find the…

A: It is given, U= {3,4,5,6,7,8,9,10}.

Q: Let A=(1, 2,3,4,5,6,7,8,9,10,11,12) how many different non-empty subsets are there in set A

A: Given,            A=(1, 2,3,4,5,6,7,8,9,10,11,12) We have to determine the number of different…

Q: (b) How many ways can the letters of the word MAILBOX be arranged in a row if M and A must remain…

A: We use techniques of basic counting to solve this question.

Q: 4 5 1 f = 4 2 3 6 7 3 6 2 7 1 (a) Write f as a product of transpositions (not necessarily disjoint),…

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Q: Define the following sets: A = {1,3,7,9,10} B = {2,5,7,8,9,10} E = {x: x is a negative natural…

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Q: Counting Permutations A permutation of the set [10] = {1,2, 3, ., 10} is a way of listing the…

A: Given set is 10=1,2,3,...,10 To find how many permutations of 10 start with k, k-1, k-2, ....,1 for…

Q: Compute f2,f3, and f-1 for each of the following permutations.   f= (l,3,7,4)(2,5,9,8,6)

A: f= (l,3,7,4)(2,5,9,8,6)

Q: Let A (k,s), t.en the power set of A is:

A: Set of all subsets of A is called power set of A.

Q: Prove that the set X= { 2,6,10,14,....} is countable Note: no handwritten

A: Prove that: The set X= { 2,6,10,14,....} is countable

Q: Let A be a set with 5 elements. If replacement is not allowed, find the number of a. 3-permutations…

A: Let A be a set with 5 elements. If replacement is not allowed, to find the number of (a)…

Q: There are n people sitting in a ring. If a person gets the keg of beer thi8 individual passes it on…

A: Given: There are n people sitting in a ring. If a person gets the keg of beer this individual passes…

Q: Let D be a set of dogs, R a set of retrievers, and G a set of golden retrievers. Assume that GCR and…

A: a) Given that G⊆R and R⊆DIf, G≠R≠D then we can say that there are some dogs which are not…

Q: Let A be a set of 16 football teams and N be a set of 16 different football teams. So A ∩ N is…

A: Respected student, by the policy of Bartleby we are answering your first 3 parts of this problem. if…

Q: Let S = {Aylesbury, Arsenal, Southend, Sheppey United, West Ham United, Maroka Swallows, Bidvest…

A: Given S = {Aylesbury, Arsenal, Southend, Sheppey United, West Ham United, Maroka Swallows, Bidvest…

Q: (a) In how many different ways can the letters of the word combine be arranged? (b) In how many…

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Q: Which of the following refers to the different arrangements of objects where some of them are the…

A: Permutation: Two different arrangements of objects where some of them are the same are identical are…

Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

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Q: Consider numbers of the form a = a₁a2a3 . . . an, with n digits, each digit from the set {1, 2, 3,…

A: For n = 15 We have to find  a. How many such numbers are there. b. How many such numbers are there…

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 2 3 4 5 6 2 3 1 5 6 4 (1 2 3 4 5 6 7 3 4 5 1 2 7 6 b. P1 = 2) and p2 = ) are the permutations on…

A: Given,  p1= 1 2 3 4 5 6 72 3 1 5 6 4 7 and  p2= 1 2 3 4 5 6 73 4 51 2 7 6 are two permutations on…

Q: The number of permutations of a set of n elements is     set in a specific order     arrangement…

A: The number of permutations of a set of n elements is     set in a specific order…

Q: Consider the following permutations in S7: (1 2 3 4 5 6 7) "- (6 2 7 5 4 1 3) The order of ß is (1 2…

A: Consider the given permutations  α and β. We need to find the order of  β. The solution is given…

Q: 4. Count the permutations 111213141516 of 1, 2, 3, 4, 5, 6} where i • 12 #1 i3 #1 1,2,3 i5 5,6 i6 #…

A: count the permutations  i1,i2,i3 i4,i5,i6 of  1,2,3,4,5,6 where i1≠1,2,3 i2≠1 i3≠1 i5≠5,6 i6≠5,6

Q: Let A = {small, medium, large}, B = {red, black}, and C = {pentagonal, round}. List the elements of…

A: Given : A =small, medium, largeB = red, blackC = pentagonal, round