2 3 4 5 6. f = 1 (i 43 5 2 6) (a) Write the permutation f' as a product of disjoint cycles, separated by commas (e.g. (1,2), (3, 4, 5),... ). Do not include 1-cycles (e.g. (2) ) in your answer. fl = (b) Determine the order of f'.

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: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8). (a) How many subsets of 6 elements does the set A have? subsets…

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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: 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: 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: f = (7 3)(14 85 37 6) g = (5 8 26143) Write each of the following permutations as a product of…

A: f = (7 3)(1 4 8 5 3 7 6)  g = (5 8 2 6 1 4 3)  (a) fg= (7 3)(1 4 8 5 3 7 6)(5 8 2 6 1 4 3)…

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: 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: Construct an example of a subset B of P({a, b, c, d}) such that (B, C) is a total ordered set.

A:

Q: Prove that n! (n-r)!r! (4) is the number of subsets (combinations) with r elements which can be…

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Q: 6. Let A = {1, 2, 3, 4} R = {(1,2), (1,3), (2,3), (2,4), (3,1)} S= {(2,1), (2,4), (3,2), (3,3),…

A: Given  A=1,2,3,4R=1,2,1,3,2,32,4,3,1S=2,1,2,4,3,2,3,3,4,3

Q: Is a permutation of one element considered to be an even permutation? For example, is (1) an even…

A: To clarify the notion of an even permutation

Q: Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Give an example of three sets, A1, A2, and A3, such that…

A:

Q: Q26. Which subset immediately precedes the subset {X7, X5, X3, X2, X1} of the set S= {X7, X6, X5,…

A: Total number of subset of S =2^8 = 256 Now let's find subsets having 5 elements. {x7,x6,x5,x4,x3}…

Q: Suppose we have a set A={1, 2, 3, 4, 5, 6}. What is the partition of A into three parts? Make sure…

A: We can partition of set A as below

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

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Q: In lectures we have seen that the set {1, 2, . . . , n} has 2n subsets. Now say that a set is…

A: Find the number of set

Q: Let A = { {a}, {b}, {c}, {d}, {e} } Determine by extension P(A

A:

Q: (a) SCR (b) 1 € R (c) 1 € S (d) 1 CU

A:

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

A:

Q: A set contains 7 distinct elements. How many subsets can be formed from the elements of S that…

A: Use combination formula

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Consider the set A = {2, 4, 6, 8} with an operation defined by the table. 2 4 6 8 2 8…

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Q: 4. Let A = {a, b, c, d, e, f, g, h, i, j, k}. (a) How many subsets of A contain exactly 8 distinct…

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

A: Introduction: A permutation is a bijective mapping from a set to itself. The general way to…

Q: Let A = {1, 2}. List all the subsets of A. Let B = {1, 2, 3}. List all the subse

A: 1. Let A=1,2find the subsets of A.2.Let B=1,2,3list the subsets of B which are not contained in A.

Q: Let U = {4, 5, 6, 7, 8, 9, 10, 11},  A = {5, 7, 9},  B = {4, 5, 8, 11}, and C = {4, 6, 10}. Find the…

A: We first find C' (complement of C)

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

A:

Q: 2. Write out the power set of the following set: {1, 2, 3, 4).

A: Solution(2)- Write out the power set of the following set say S={1,2,3,4}

Q: raw the Hasse di

A: Given, the poset x is a divisor of on the set                           {1, 2, 3, 5, 6, 10, 15, 30}…