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

Q: a) Let S={a, b, c}, and for each integer i= 0, 1, 2, 3, let S, be the set of all subsets of S that…

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Q: True or False: Given set A, if B is an element of P(A), then BC A

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Q: Show that An (B U C) = (Ñ n B) u Ā - Using membership tables.

A: Solution:

Q: What is the cardinality of the set of 2 x 2 matrices over N? Prove your answer.  Note: a 2 x 2…

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Q: Show that, for given integers a, b, c, if gcd(a, c) = gcd (b, c) = 1, then gcd (ab, c) = 1

A: Given a,b,c∈Z+ And gcda,c=1 and gcdb,c=1 We have to show that gcdab,c=1 Since, gcda,c=1 and gcdb,c=1…

Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

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Q: If C ={}    is {} an element of c

A: The problem concerns understanding the definition of the empty set

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: Find the orders of all the elements of U₁8. Is U18 cyclic?

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Q: B. Let A = {7,8,9}, {1,2 determine all the elements of: 1. AUD 2. (DOC) U An B ,4,5,6}, {2, 4, 6},…

A: The provided information is as follows:Sets are as .The universal set is

Q: Show that the subset [2,5] [7,9] of R has exactly 4 clopen subset.

A: The question is wrong.

Q: Prove that if A – B – D and B – C – D, then A -C– D.

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Q: required to prove that A×∅=∅

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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: 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: Exercise 14.4.28. Express the following permutations as products of trans- positions. (a) (14356)…

A: Given: d)(17254)(1423)(154632) f)(13579)(2468)(19753)(2864)

Q: Suppose that 2 = {1,2,3,4} and C = {{1}, {2}, {3,4}}. Determine o(C), the smallest o-algebra on 2…

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Q: uppose that A ⊆ C so that n(A) = 5 and n(C) = 11. How many subset B, with n(B) = 8 are there such…

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Q: let A= {y is an element of Z; y=6b-4 for some integer b} B= {x is an element of Z; x=3a+2 for some…

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Q: Answer true or false to each of the following (show your work):

A: 5.  a) p(3) is "17&lt;25" which is TRUE. b) p(2) is "12&lt;25" which is true and p(5) is "27&lt;25"…

Q: Say that X ⊆ R is closed under multiplication if for all x,y ∈ X, we have that xy ∈ X. Give three…

A: 1 A=0,10×0=0∈A, 1×1∈A, 0×1=0∈A B=-1,1-1×-1=1∈B, 1×1=1∈B C=-1,0,1-1×-1=1∈C, 1×1=1∈C,0×0=0∈C,…

Q: On the set A={a,b,c,d} the table gives the folowing operation: (picture) Is (M,o) semigroup?

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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: Prove that there is an (v, k, X)-design with b blocks and each element appearing in r blocks if and…

A: The problem at hand deals with the concept of designs and aims to establish a relationship between…

Q: The_____ of A and B consists of all elements in either A or B or both.

A: The_____ of A and B consists of all elements in either A or B or both.   The answer of the above…

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: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

A: A proper subset of a set A is a subset of A that is not equal to A.Or in other words, if B is a…

Q: Let z, y, z be integers. Prove that if z +y + zis odd, at least one of z, y, or z is odd.

A: We prove this by contradiction

Q: Find the GCD and LCM for each of the following groups of numbers using the intersection-of-sets…

A: GCD (Greatest Common Divisor) of two numbers is the largest number that divides both of them.  And…

Q: Compute A∪B, A∩B, B\C, and (A∩B)\C where A={2,3,5,7,11,13}, B={2,3,4,5,6,7,8,9,10,11,12}, and…

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Q: raw the Hasse di

A: Given, the poset x is a divisor of on the set                           {1, 2, 3, 5, 6, 10, 15, 30}…

Q: Write down four distinct elements of the set {z ∈ C : z − z ̄ = 2i}.

A: The given set is z∈ℂ:z-z=2i We have to find the four distinct element of the given set.

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

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