Find an element in A12 of order 30.

Q: (iv) The power set P(C) of C by listing down the elements directly.

A:

Q: List all the elements of S4, written in cyclic notation.

A: To list out all the elements of S4.

Q: 5. Show that M:= {ECR: E is countable or E is countable} is a o-algebra.

A:

Q: (D) Let s be an integer such that 1 ss < 104651 and 24578° mod 104651 = 3190 Find s and explain how…

A: Let s be the integer such that and Purpose: To find the value of s

Q: Compute C7,2. (Enter an exact number.)

A: A combination is a selection of all or part of a set of objects, without follow any order in which…

Q: Compute the following.   8C3=

A:

Q: Given any whole number w, how many whole number triple decompositions does w have? Prove it.

A: A number is said to be whole when it begins from 0 and has no end. Decomposition of number means…

Q: Identify the notation used for each of the following concepts. a. k factorial b. The number of…

A: a. k factorial is denoted as k!

Q: Show that A8 contains an element of order 15.

A:

Q: In (Z24, €) find the orders of the elements 3, 4, 6, 7, and 18.

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 7. Calculate each of the following. [from #22, 4.5] b) 971321 (mod 765) a) 2557341 (mod 5681)

A:

Q: Compute (12.3 - x) for the following set of n = 5 values. X1 = 0, x2 = 2.9, x3 = 5.5, x4 = 0.4, x5 =…

A: Use the given information to obtain the objective of the problem.

Q: Compute C7,5. (Enter an exact number.)

A: We know that Combination formula: Cn,r = C(n,r) = nCr = n!/(n-r)!r!

Q: Find the least residue of 448 modulo 7

A: Given problem is : Find the least residue of 448 modulo 7

Q: Identify the significantly different pairs in the Tukey output below

A: The pairs are said to be significantly different if corresponding p value is less than 0.05

Q: Derive a formula for E-1 Qiwhere Qi represents number of edges of n-dimensional cube and prove the…

A: As indicated, we shall use mathematical induction.

Q: Find the multiplicative inverse of the given element   [9] in Z242

A: To find the multiplicative inverse of the given element 9 in Z242.

Q: 1) Find the number of permutations of all the letters of the w following conditions

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

Q: Determine which elements of Z8 have inverses under the op- eration ×8. Then do the same for Z7 under…

A:

Q: The number of substrings (of all lengths inclusive) that can be formed from a character string of…

A: A string is a set of characters. A substring is a set of characters that can be formed by taking 1…

Q: Use the method of Example 9.5.11 to answer the following questions. (a) How many distinguishable…

A:

Q: How many elements are there in the greatest conjugacy class of 5 ?S

A:

Q: Show that the permutations (12) and (12345) generate S5.

A:

Q: Find the order of [5] in Z23

A:

Q: Compute the following. 5! 4!

A:

Q: Determine whether each of the strings of 12 digits is a valid UPC code.a) 036000291452 b)…

A:

Q: 13

A: Consider the integral

Q: WIKS the largest order of an element in the groupof permutations of 4 objects!

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

Q: 5. For each of the following pairs of numbers a and b, calculate gcd(a, b) and find integers r and s…

A:

Q: Which of the following numbers could be the exact number ofelements of order 21 in a group: 21600,…

A: According to theorem, the number of elements of order n in a group is multiple of ϕ(n)

Q: Compute the following. 6! %3D O!

A: Compute 6!0!=?

Q: Suppose that in a certain state, all automobile license plates have four letters of the 26 English…

A: GivenAutomobile license plates have four letters and followed bt three digitsNo.of letters from A-Z…

Q: Prove that if c is a natural number then for all a and b we have : gcd(ac, bc) = c gcd(a, b)

A: We have to prove that if c is a natural number then for all a and b gcd(ac, bc)=c gcd(a, b) .

Q: Which of the following is cyclic? * O U30 O U50 O U20 O U40

A: B is the option:-U(50) As per the guidelines we can only solve one question at a time. Thank you.

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: Compute the following: N!(N-4)!

A: Note that n!=n×n-1×n-2×…×3×2×1. Consider the given expression N!N-4!. This can be written as…

Q: If possible, give an example of an element of Ag that has the given order; if there is no such…

A: According to the guidelines i solve first 3 subpart so kindly request you to repost the remaining…

Q: Let p = 17 and d be a divisor of o(p). Determine (d) for each d. List each element having order d,…

A: Given : p=17 and d is a divisor of ϕp To find : ψd for each d and list each element having order d,…

Q: Let β element of S7 and suppose β^4=(3567214). Find β.

A: Given:         let β∈S7         β4=3567214   note that β is a 7 cycle.   Thus , β has order 7.

Q: Compute |A| for the following:

A: Given: A=234124431

Q: : The Wronskian of e" , e2¤ Add a caption... > Status (Custom)

A:

Q: How many elements of order 4 does Z4 ⊕ Z4 have? (Do not do this by examining each element.) Explain…

A:

Q: Find the largest possible order of an element in S7.

A:

Q: Construct the multiplication table for Zs. Using this table, or otherwise, determine the following x…

A:

Q: Determines the equivalent number, according to the indicated module, for the following numbers: a 19…

A:

Q: In N, where N is a set of natural numbers, multiplication by '.' Identify the reversible elements.

A: Query-  In N, where N is a set of natural numbers, multiplication by '.' To Identify- The reversible…

Q: Find the order of the element 5(9)in the factor group U(16)/(9).

A:

Q: How many different orders are possible in Z*92639 (Hint: 91639 is a prime; 91638=2 . 27 . 1697).…

A: as 92639 is a prime number so Z*92639 is cyclic group of order 92638.

Q: To index Qn [6, 20] using N as the index set.

A: We need to find ℚ∩6, 20 and we have the index set is ℕ Now, ℚ∩6, 20=6, 20