The number of the element(s) of order 2 in Z3 O Z6 O 2 3

Q: if A) B) none of these a(n) a(n) is smaller or equal to oo then is finite

A: In the question we have to select correct option.

Q: 2. (a) Find integers a, m, n such that m | a and n | a, but mn /a.

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Q: n = n and n = 1. n Show that in

A: A factorial is the product of consecutive integers starting from 1. It is known that nr represents…

Q: B. Find e in the whole number. 1. N = 5,000 2. N = 20,000 3. N = 12,000 and n = 200 and n = 3,000 e…

A: B. Here we have to find e in whole number. Formula to calculate e is as,…

Q: Find the value(s) of such that х -1 2х 1 -1 0=12 2 -1 -x O x=4 or x= -3 O x= -4 or x = -3 O x= -4 or…

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Q: The number of the element(s) of order 2 in Z2 O D6 12 1 11 7 15 24 None of them

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Q: An instructor of mathematics wishes to determine the relationship of grades on a final examination…

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Q: How many elements are in Z5[i]/<1 + i>?

A: Given Data The expression is Z5[i]/<1+i>.   Consider the Z5[i]/<1+i> in the form of…

Q: (a) an = }(n² + n). (b) an = 2an-1 – an-2 with ao = 0 and aj = 1. (c) an = nan-1 with ao = 1. %3D

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Q: 5. Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n ≥ 3, an = 2an-1+ bn-1 for n ≥ 2 bn = bn-1 + an-1…

A: Given Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n ≥ 3, an = 2an-1+ bn-1 for n ≥ 2 bn = bn-1 + an-1…

Q: k = 4 4. Let k be the second smallest nonzero digit of your Student ID. Compute the order of (k, k)…

A: To find the order of (4,4) .

Q: Find the elements (a, b) of G of order 2. O Show that G has no element of order 3.

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Q: The coefficient of xy13 in the expansion of (x + y)¹8 is O 43,758 O b 31,824 18,564 8,568 C Od

A: We know (r+1)-th term of binomial (x+y)n is  Tr+1=Crnxn-ryr

Q: Σ 9n n = 1 Identify an-

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Q: The order of the element 16+ in Z24/ is None of the choices 1 4 8.

A: The order of an element a in a group Gis the number of elements in the cyclic subgroup of G.  Also…

Q: The number of the element(s) of order 2 in Z2 O D6

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Q: The characteristic of Z[x] is None of the choices Оз O 5 O 6

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Q: 4. Let, a, = 1, az = 2, b, = 0, b2 = 1, for n 2 3, an = 2an-1+ bn-1 for n 22 bn = bn-1+ an-1 express…

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Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" %3D (1.112) n = nk"-1 kn~2…

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Q: @31 Find the nverse of the functions 1) fex) = 2x-1 2メ+) 2) fa)

A: The given functions are a fx=2x-1bfx=e2x+1We need to find the inverse of the above functions.

Q: (a) Find all the irreducible representations of S3.

A: To Determine :-  All the irreducible representations of S3.

Q: nd all values of z for which zª + 2 – i2/3 = 0 and represent them geometrically. |

A: To solve the given equation by using D'Moivre theorem we find the point. The 4 value of z satisfy…

Q: Write all elements of S4. Show that S4 has no elements of order > 5.

A: The given question is related with abstract algebra. We have to write all the elements of S4 . Also,…

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: 2 Let M 2 8 Find formulas for the entries of M", where n is a positive integer. 1001 100 J M" = 27

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Q: Let, a1= 3, a2 = 4 and for n ≥ 3, an = 2an-1 + an-2 − 5, express an in terms of n. 5. Let, a1 = 1,…

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Q: Find the elements of Z24 of order 8. (Hint: o(1)=24)

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Q: Factor 19 into irreducible elements in the Gaussian integers, Z[i].

A: We have to factor 19 into irreducible elements in the Gaussian integers, ℤ[i]. Irreducible element :…

Q: Select all of the following that are equivalent to >(2) +> (3k + 1)? k=0 k=0 п+1 A. O) (3k + 3) k=0…

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Q: Find the values of z for (k=1 and k=4), if z=(-1)9 1-i/3 and -1 2. 1+i/3 and -1 1+i/3 and -i 2…

A: De Moivre's Theorem for fractional power:                                           (cos(θ)+i…

Q: The number of the element(s) of order 17 in Z17 O Z17 288 16 17 None of them 289

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Q: ni = 22, î1 = 99.2, ô1 = 4.5 n2 = 35, îz = 82.6, ô2 = 4 Using the information above, compute the…

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Q: Find the least value of “n" so that , k=n 1 199 Sn 2k-1 k=1 200

A: Given:          Sn=∑k=1n12k−1>199200

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

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Q: The element (3x-6) is Reducible over QO lucible over Q and R c. Both d. Other O O O O

A: The elements (3x-6) is_____

Q: 5 = t(n + 1) = t(n +2) = t(n + 3) holds for n = 3655 and 4503. (a) Verify that t (n) (b) When n =…

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Q: The principle of mathematical induction can be formally represented as [P(1)V vk( P(k) → P(k + 1))]…

A: Q1.The principle of mathematical induction can be formally expressed as P1∧∀kPk→Pk+1→∀nPn. Hence,…

Q: a) Prove that ε n(n+ 1)(2n + 1) Σ 6 i=0

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Q: Select the correct comparisor 1 Σ n=1n2 +5 Select one: a. Non of them b. Σ 2" n =1 C. n2 n = 1 d. Σ…

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Q: 1) Find all associates of (i) [6] in Z10, (ii) [4] in Z5.

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Q: Question 11 of 20 There are 17 players on a Calvinball team At the start of the game, the 13 players…

A: There are 17 players on a Calvinaball team. At the start of the game, the 13 players on the field…

Q: The number of generators of Z15 is 7 8 O O

A: ℤ15 is a finite group.we have to find number of generators in ℤ15

Q: .In Z[V-5], the element 29 is: O Unit O reducible Irreducible None of the choices

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Q: Let Z - N(0, 1). Find P79.1 of Z Select one: O a. 0.44 O b. -0.81 O c. -0.44 O d. 0.81

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Q: 2. In a certain shopping mall, restaurant charges are P125, P150, P200, P165, P175, P190, P230, and…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: a) Expand Ca-b)Catb) b) Hence, expand ox-y+2)(ctytz)

A: a) Expanding (a - b )(a + b)  (a - b)(a + b) =  a(a+b) - b( a+b)                        =  a.a + a.b…

Q: Find all m, n E N such that: n! + 2n + 49 = m²

A: This problem can be solved by graphical approach. Use a graphing utility to plot the graph of…

Q: 4. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2+n², express an in terms of n. 5. Let, a1 = 1,…

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Q: Use the factor theorem to verify the statement

A: Given statement is, x+y is a factor of xn-yn for every positive even integer n.   So, Let fx=xn-yn,…