If B and C are subsets of Z closed under addition, then BUC is also closed under addition.

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: If A is a perfect subset of B and P(a < Pb), then P(BA) is equal to O a. P(a) / P (b)

A: Given: A is a perfect subset of BP(a &lt; Pb)

Q: Prove that if x, y, z is a Pythagorean triple, then at least one of x and y is divisible by 3, and…

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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: a. Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and…

A: # we are entitled to solve one question at a time. Please resubmit the other questions of you wish…

Q: If A and B are partitions of [a,b] and ||A|| < ||B||. then ВСАФ B not subset of A A not subset of B…

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Q: Determine if the following sets are closed under multiplication. a. (1,18) b. {2k + 9|keW} c.…

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Q: In each of (a)-(f), answer the following questions: Is AS B? Is B C A? Is either A or B a proper…

A: As per the policy of bartleby the provisions is to solve only one 3 subparts of questions at a time

Q: required to prove that A×∅=∅

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Q: 3. Suppose a set S contains 9 positive integers, none of which is larger than 50. Show that we can…

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Q: Consider the set Z, × Z, = {(x, y) : x € Z, and y € Z3}. Define the operation/sum O in Z2 × Z3 such…

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Q: Let A = {small, medium, large}, B = {blue, magenta}, and C = {pentagonal, round}. List the elements…

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Q: Show that the following subset of R is countable: {m +n/2: m, n E Z}.

A: Fairly simple Z is countable set and as so set is , so now clearly we have a bijection    and that…

Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: If a and b are even then GCD(a,b) must be 2

A: Given statement :- if a and b are even then GCD(a,b) must be 2

Q: Suppose we have a set A={1, 2, 3, 4, 5, 6}. What is the partition of A into three parts? Make sure…

A: We can partition of set A as below

Q: Prove that if n divides a, b, and c, then n³ divides a²(b – c) + b² (a – c) +²(b – a).

A: A product is a multiplication of two or more terms and these terms are called the factors of the…

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

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Q: Let Z denote the set of integers. If m is a positive integer, we write Zm for the system "integers…

A: Given system:.To find:a) Name the systems, which satisfies the following operations.i) ii) iii)…

Q: A set contains 7 distinct elements. How many subsets can be formed from the elements of S that…

A: Use combination formula

Q: The greatest common divisor c, of a and b, denoted as c = gcd(a,b), is the largest number that…

A: Here is the solution

Q: Set A contains 45 elements, set B contains 52 elements, and 15 elements are common to sets A and B.…

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Q: Prove that the following 2 sets are equal: {4k + 5 : k ∈ Z} = {4k + 1 : k ∈ Z}.

A: Two sets are equal if and only if They have the same element  We are using here if x €A. &lt;=&gt;…

Q: let A, B ⊂ R, and suppose A and B are closed. Prove that A ∩B is closed. Hint: You might try showing…

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Q: If A is a subset of B, and B is a subset of A, then does A=B?(Y/N) If A maps onto B, and if B maps…

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Q: Let A = ({0} ∪ {x | x ∈ ℤ+and x < 4}), B = {0, 1, 3, 5, 7}, and C = ({0} ∪{x | x ∈ ℤ+and x is even…

A: Since you have posted a multi subparts question according to guildlines I will solve first(a,b,c)…

Q: Consider the set A = {2, 4, 6, 8} with an operation defined by the table. 2 4 6 8 2 8…

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Q: B1. b. Construct the Multiplication Table of Congruence Class Zs

A: We have construct 6×6 table

Q: Use a three-ring, eight-region Venn diagram as a reference and determine whether (A′∪B)∩C′=A′∩(B∪C′)…

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Q: Let A = {small, medium, large}, B = {red, black}, and C = {pentagonal, round}. List the elements of…

A: Given : A =small, medium, largeB = red, blackC = pentagonal, round

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: if C={}         is {} subset of C ?

A: Question: Is the empty set a subset of itself?

Q: 2. Prove thatN is the smallest inductive subset of R:

A: We can prove this by proving property of induction

Q: . List all integer partitions for n = = 5, and find the conjugate for each partition.

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Q: Find the number of triples (A, B, C) of subsets of [n] such that at least one of A ∩ B, A ∩ C, or B…

A: Set theory