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), separated by commas (e.g. (1, 2), (2, 3),... ). f = (b) Write f- as a product of transpositions in the same way. f-1 = %3D Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so (1, 3)(1, 2) = (1,2, 3) not (1,3,2).

Q: . How many 4-membered subsets can be chosen from {1, 2, 3, 4, 5} if repetitions are allowed?…

A: Number of ways to choose r numbers from a n -set is nCr

Q: Find out how many distinguishable permutations are in the following words. Population

A: The given word is "population"

Q: Let U =  {2, 3, 4, 5, 6, 7, 8, 9},   A =  {3, 5, 7},   B =  {2, 3, 6, 9},  and C =  {2, 4, 8}.…

A: Given U = {2, 3, 4, 5, 6, 7, 8, 9},   A = {3, 5, 7}, B = {2, 3, 6, 9}, and C ={2, 4, 8}. Find  (A ∪…

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

A:

Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: How many subsets does the set L= {6, 7, 8, 9} have? %3D

A: A is called the subset of B if all the elements in A are also present in B. In the given set L there…

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?…

A:

Q: Let S=(1,2,3,4,5,6,7,8). How many permutations are there if: a. The odd and even numbers trade…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Suppose U = {1,2,3,4,5,6,7,8,9,10}, A = {2,4,6,8,10}, and B = {2,3,5,7}, which values are in A…

A: We have given that,  U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } A = { 2, 4, 6, 8, 10 } B = { 2, 3, 5, 7 }

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: 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: Let S = {1, 2, 3, 4, 5, 6, 7, 8},  A = {4, 6, 7},  B = {2, 3, 4, 8},  and  C = {2, 4, 5, 6}.  List…

A: We have to solve given problem:

Q: A(n) _______ is an ordered arrangement ofr objects chosen from n objects.

A: We fill the blank space as

Q: Let U={1,2,3,4,5,6} be the universal set and A-{2,4,6}. Then the power set of the complement of U…

A: Given that  U={1,2,3,4,5,6} and A={2,4,6} To find The power set of the complement of U.

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: 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: Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7, 8, 9}, defined as follows f = (31…

A:

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: The following table shows the number of new (single-unit) houses started, in thousands, in the…

A:

Q: If A is a perfect subset of B and P(a > Pb), then P(A - B) is equal to O a. O b. O c. O d. P(a) /…

A: To determine the value of p(A-B) where A is a perfect subset of B.

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

A:

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

A:

Q: What is (A∪B)c where A={5,11,3,8,9} , B={99,5,11,2,4} and Universal Set…

A:

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…

A:

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 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: Let X = the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on…

A: We have given that  Let x = the number of non zero digits in a randomly selected 4 digit PIN that…

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: 2. Determine the power set of the following sets: (a}{1,5} (b){a,b,c,d}

A: The power set is a set of all the subsets. a) A=1,5Then,PA=ϕ, 1, 5, 1,5

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: * Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7, 8, 9}, defined as follows f = (3 1…

A:

Q: what is the permutation of (1 10 12 3)(2 9 11 13)(1 7 15 10)(8 20 14 9)(1 3 12 10)(2 13 11 9)(1 10…

A: According to the given data, find the permutation:

Q: 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

A: Given:

Q: Let o be the permutation defined by: 1 2 3 O = 14 9 10 2 12 6 5 11 15 3 8 7 4 1 13 4 5 6 7 8 9. 10…

A:

Q: {1, 2, 4, 8, 9, 10, 16} and Y = {3, 4, 7, 9, 15}, then X ∩ Y is ________. {1, 3, 6, 7} {4, 9} {3,…

A: The intersection of two sets contains the common elements of both sets, i.e., the values in the…