(3) Let σ= 123456789 365149872 in Sg (a) Compute o2 and 0-1 (b) Write o as a product of disjoint cycles (c) Compute |o|, the order of o (d) Write o as a product of transpositions (e) Is o even or odd? σ

Q: Show that the middle term in the expansion of (1 + x)2¹ is (1-3.5 (2n- -1)) 2"x", where n is a…

A:

Q: Let n be a positive odd integer number (i.e., n = 2k + 1, for some integer k). Find a unit fraction…

A: To find: Unit fraction representation of 3n, for any positive odd integer n.

Q: m and n, mn, such that: and U(m) ~U(n). Find integers a) |U(m)| = |U(n) b) |U (m)| = |U(n) and U(m)…

A:

Q: Show that the k-cycle (1 2 · · · k) cannot be written as a product of fewer than k − 1…

A: We have to prove that the k-cycle (12…k) cannot be written as a product of fewer than k−1…

Q: QUESTION 12 Given a = (1 3 5 6 7)(2 3 5 6 7) in Sg. a) (3) Write a as a cycie or a product of…

A:

Q: 4 Let f = (4 5 6) and g = (1984) (275) (36) be two permutations in S9. (a) Compute fogo f-1, and…

A: Let       given cycles f and g from S9 .

Q: (f) Write down, in cycle form, the elements of the cyclic subgroup H of So generated by p. (g) Write…

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Q: The permutations P = p and q in So have the two-line symbols 1 2 3 4 5 6 15 2 3 4 6 1 2 3 4 5 6 4 6…

A: We can find the given permutations in cycle form and order.

Q: Prove that o – 1 is divisible by 4.

A: Even numbers are numbers divisible by 2. Odd numbers are numbers that are not divisible by 2. The…

Q: *discrete math* Prove that for all integers a, b, if a and b are congruent to 1, mod 3, then their…

A: An integer n is congruent to 1, mod 3, if and only if there is an integer k such that n = 3k + 1.

Q: 05. Write in sigma notation: 2 + 4 + 6 +8 + i-1 8 X2i =] 2i 22 i=0 0 16 i=2 + 16

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Q: 25 Describe a sequence of transformations that will map AABC onto ADEF as shown below. B E F.

A: Answer is mentioned below

Q: Question 6 Prior to running the Boston Marathon, a runner's personal best pace for a race is 10…

A: Given that Prior to running the Boston Marathon, a runner’s personal best pace for a race is 10…

Q: 3. Suppose b > 1 is an integer. The proof of the existence of a base b representation of any integer…

A: (a)

Q: The permutations p= p and q in So have the two-line symbols 1 2 3 4 5 6 15 2 3 4 6 1 2 3 4 5 6 4 6 2…

A:

Q: (a) Find an integer n > 2 such that all nonzero elements of Zn have multi- plicative inverses. (b)…

A:

Q: 3. How many zeros at the end does the number 2022! have? (n! is a product of all positive integers…

A: Given,Number = 2022!To find: Number of zeros at the end (trailing zeros) of the given number  As per…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: QUESTION 13 List all the elements of order 12 in Z600.

A:

Q: A) Express the following using favtorials and simplify: ([n] [2]). B) Show the following using…

A: Consider the combination n r as nCr. Note that, nCr=n!r!×n-r!. A) n…

Q: Prove or disprove: For n > 2, n − 1 is a generator of U(n)

A:

Q: Consider the Fibonacci numbers {F, = 1, F2 = 1, F3 = 2, F4 = 3, Fs = 5, F6 = 8,· ·}. Prove by…

A: I have given the proof in second step

Q: (12) (13) (14) (15), (123) (234) (345),

A: This is a multiple questions.

Q: QUESTION 5 Find all the elements of order 12 in Z48000 -

A: Number of elements of [m] in Zn is phi(m)

Q: Select the decimal representation for (407) 16. 0 261 0263 O 2560 02567 MacBook Pro

A: