Can a group of order 55 have exactly 20 elements of order 11? Givea reason for your answer

Q: Produce the least positive number that is divisible by​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, and 11.…

A: Given Produce the least positive number that is divisible 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11.…

Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

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Q: 1. Let A = {2, {2},{{2}}}, B = {2, {2}, {2, {2}}}. Is A C B? Is BC A? Is either A or B a proner…

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Q: How would you write a formal proof for if AnB = B then B is a subset of A?

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Q: Which of the following is the set of terminal symbols? OV = {S, A} {a,b} = {S → aSb|\} T = P = T =…

A: In formal language theory, a formal grammar is a mathematical model used to describe a language. It…

Q: The numbers 1, 2,..., 12 can be entered into the 12 regions of the diagram to the right so that each…

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Q: Find the orders of all the elements of U₁8. Is U18 cyclic?

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Q: QUESTION 7. Find the number of permutations of length 9 that satisfy the following conditions: (i)…

A: To find- Find the number of permutations of length 9 that satisfy the following conditions: It…

Q: There are lots of ways to split the integers into two sets whose intersection is empty. An example…

A: Let, A= { integers greater than or equal to 0}  and B={ integers less than 0}

Q: Consider a group of n distinct individuals or objects. An umordered subset of the group is called a…

A: Given that there are seven choices of additional toppings: Mushrooms (MU), Menma (ME), Green Onion…

Q: »pr«°C =m•22=4

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Q: D 2.141 Show that for any positive natural number, the sum 12+1212+121212+...+121212...12 4 100"* —…

A: Applying the sum of GP, geometric progression.

Q: Use Venn diagrams to demonstrate that (An B) -CCANCC.

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Q: nti Sacies

A: We apply the series method for following question

Q: The number of the element(s) of order 13 in Z13 O Z13 12 None of them O 13 169 168

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Q: Question 4. elements a, b, and c are distinct) Explain your answer. (a) Ø (b) {0, {a}} (c) {Ø, {a},…

A: The power set of a set S is the set of all subsets of S, including the empty set and S itself. In…

Q: 8. How many ways are there to seat four of a group of ten people around a circular table where two…

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Q: Which groups Un are cyclic for n in the range 50 ≤ n ≤ 60?

A: For the range 50≤n≤60, the cyclic groups Un​​ are those with n=53and n=59, since these are prime…

Q: Let the universal set U = {Meansville, Molena, Stockbridge, McDonough, Hampton and Locust Grove,…

A: Given that,  The universal set is: U=Meansville, Molena, Stockbridge, McDonough, Hampton and Locust…

Q: Question 2 (Cyc Given positive integers a1, a2, ...,ak with a1 + a2 +...+ ag = n, how many…

A: Given that there are a1,a2,...,ak positive integers. Also a1+a2+...+ak=n. Without loss of generality…

Q: List the subsets of set Q given that Q={w,x,y,z}. no element How many such subsets? one element only…

A: Please see the below picture for detailed solution.

Q: Find an element in A12 of order 30.

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Q: What is the largest order of an element in the group of permutations of 4 objects?

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Q: Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered…

A: Given that: n(A)=p, and n(B)=q

Q: Consider all n! permutations of the set {1,2,3,..., n}. We say that a number i is a fixed point of a…

A: Given: pn(k) be number of permutations of 1, 2, ..., n that has exactly k fixed points.

Q: Ι p(2) = 5 }. . ρε S, 1

A: concept: We have to find all those elements of permutation group (S5) that map 2 to 5.

Q: Consider the two image subsets. S, and S, shown in the Following figure. For V {1}, determine…

A: Given: