Draw the Hasse diagram of all positive divisors of p³q*.

Q: Find the number of elements in the conjugacy class of (abc)(def) in S₆

A: We have to find the number of elements in the conjugacy class of (a b c)(d e f) in S₆

Q: 2. U={x|x is an integer, 2<x<10}. A and B are subsets of U such that A= {multiples of 3}, B={factors…

A: Using set theory we have to answer following.

Q: greatest common divisor(g.c.d)

A:

Q: 8. Find the number zeroes with which the decimal representation of 6000! terminates. (a) 1472 (b)…

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Q: Prove that the order of 3 modulo 19 is a divisor of 18.

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Q: Exercise 6D Use this Venn diagram to answer Questions 1 and 2. Members of youth club (U) Greg lays…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What are the two things we need to show to prove that need to show to prove that is a binary…

A: To find: the conditions such that "*" is a binary operation or binary composition.

Q: Prove that for any integer n, we have n - 2 is not divisible by 4.

A:

Q: 4. Show that for all positive integers n, n! + 1 has a prime divisor greater than n.

A: Let n be an integer such that n&gt;1. All prime divisors of n!+1 must be bigger than n. This is…

Q: Is this a binary operation on the set of all positive integers? r*s = qt where q and t are both…

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Q: d. y= x² + y x + cos y

A:

Q: List all common divisors of each of the following pairs of integers 24, 32

A: Given(24,32)To list common divisors of above

Q: 8) Prove that n³ + 2n is divisible by 3 for any natural n. 5

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Q: A binary string is a word containing only Os and 1s. In a binary string, a 1-run is a non-extendable…

A: def count_1_runs(n): binary_representation = bin(n)[2:] # get the binary representation of n…

Q: List all elements of (Mat. (2/22)

A: We can list all the elements.

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

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Q: 3. We say that an integer c is a common divisor of integers a and b if cla and cb. We say c is the…

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

A: (a)

Q: Use Pascal's Triangle to expand the binomial (x + 1)° O 25 + 5x4 + 10x + 10x2 + 5x + 1 O g5 - 5x1-…

A: Pascal's triangle…

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

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Q: prove that n²_1 is divisible by when ever n is odd an Positive integer.

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Q: Find all divisors of 20.

A: The given number is .The aim is to find the divisors of .

Q: 4. Does 3 divide (3k + 1)(3k + 2)(3k + 3)?

A: We will show by induction, put the value of k = 0 we find, (3x0+1)(3x0+2)(3x0+3) = 6  Which is…

Q: 10. Prove that n³-n is divisible by 6 for every integer n.

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Q: Let m and n are relatively prime, positive integers. What is the greatest common divisor of 5m + 7m…

A: Since m and n are relatively prime, we can use the following property: For any two relatively prime…

Q: Describe all extensions of the identity map of ℚ to an isomorphism mapping ℚ(3rd root of 2) onto a…

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Q: Prove: Any positive integer can be represented as an aggregate of different powers of 3, the terms…

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Q: Prove that n2 + 4 is not divisible by 3 for all integers n.

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Q: Find all positive integers n such that the sum of all positive divisors of n is odd.

A: Given the data

Q: 10. Construct the operation table for each of the following: (a) (Zg, +), (Zg, ), and (Ug, ) 11

A: Introduction: “Since you have posted multiple questions, we will provide the solutiononly to the…