1. Let A be a set, and Bi, i € I be a family of sets indexed by I. Prove De Morgan's laws: (i) A\ (Uici Bi) = nieI (A\Bi) (ii) A\ (ni B₁) = Uic1 (A\B₁)

Q: Let A = {x € N|x < 7}, B = {x € Z] -4 < x-2<4}. And C = {x E R|x² + x - 12 = 0}. a) List the…

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Q: ieN (4 For each nEN, let A, = {-2n,0,2n}. (a) UA; = (b) NA: = ieN ieN

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Q: Let U = R be the universal set and A = [1,3], B = (-∞,6], C = (-4,0). a) AUB b) BnC c) A-C d) BC

A: Let  be the universal set and  Then we have to answer the following...

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A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

Q: 1. Let A, B abd C be sets. Prove that Au (B-C) = (AUB) - (C-A).

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Q: [2, 5]U[3, 7] [2,7]

A: Let A=[2,5]and B=[3,7]and we have to prove that AUB=[2,7]

Q: |x²| = p^ n

A: Given: X=pWe need to show that Xn=pn

Q: 17. Prove: S' is a closed set.

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Q: Question: 7. Suppose A and B are sets in universe U. Prove that An (AUB) = B\ A.

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Q: 1. a) Suppose A, B and C are sets. What do you need to show to prove the following using the…

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Q: Let A, B and C be

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Q: Question 11. Let M = (A - B) n (A - C) and N = A - (B nC) where A, B, and C are sets. Using the til…

A: INTRODUCTION:  A collection of well defined distinct elements is called a set. If the two sets have…

Q: 2) Let K be any Boolean algebra. A useful relation y (read as "x precedes y" ) if and only if xy=x.…

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Q: Prove that if A and B are sets, then (A∩B)∪(A∩B^' )=A

A: To prove : A∩B∪A∩B'=A   Let x∈A∩B∪A∩B' ⇒x∈A∩B or x∈A∩B' ⇒x∈A and x∈Bor x∈A and x∈B' In either of the…

Q: If a universal set has 500 elements, n(a)= 240, n(AUB) = 400, n(An B) = 55, what is n(B')?

A: Total number of elements = n(U) = 500n(A) = 240n(A  B) = 400n(AB) = 55We have to find n(B').

Q: 2) het A, B and non- dijoint diagranı be Three Cveyla Ony using sets von Show (B-C)Ule- A) # A-8

A: firstly, we will draw all given set region then we comparing both side

Q: 3) Prove using Venn diagram that An (BUC) = (An B) U (ANC) 4) Using equality of sets, prove that (A…

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Q: VI. De-Morgan's Laws : If A, B and C are any two sets, then (i) (A U B) = A'O B' (ii) (An B) = A'U…

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Q: Establish the following set theoretic relations: a) AUB=BUA, ANB=BnA (Commutativity) b) AU (BUC) =…

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Q: Choose the best option that answers each problem. You may choose only one. 1) Let R be the set of…

A: To Choose : The best option that answers each problem.Let R be the set of all subsets of a set X.…

Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: -9 3 out of [3]--- [14] = {-4} {[6]]]} . You need to choose the correct answer or enter the required…

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Q: ieN 5. (a) Uli,i+ 1]= (b) Nli, ieN ieN 6. (a) | Iro.i +11=

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Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

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Q: For an indexed collection of sets to have an intersection an element needs to be in every set right?…

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Q: 1) Let f: A ->B with C1 C C2C A and Dic D,CB Which is true? a) f(C) c f(C2) OR b) f(C2) c f(C:) (i)…

A: Given: i) To prove that answer is correct. ii) To give a counterexample to show that the set…

Q: Find the Car D={a, b, c, d, ..., z), n(D)=? U=universal set n(U')=? B={p people in the USA | p is a…

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Q: a) veriry one of DeMorgan's Laws for sets! {S\U: U €U} = S \ U{U: U €U}. b) Show that the…

A: This is a question of topology.

Q: Suppose A, B and C are sets. Prove that A\ (BC) = (AB) U (ANC). [Prove this using elements of these…

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Q: Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-1)-1 = R. (b) (RUS)-1 = R-'Us-!.…

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Q: I) We know that -5,-4,-3,-2,-1? and IN are well-ordered sets with respect to the trivial ordering.…

A: Solution: Given the sets -5,-4,-3,-2,-1 and ℕ are well-ordered with respect to the trivial ordering.…

Q: 3.) Nowe consider motrix cif possible) as a linear combination of the motrices in' ls. the set s…

A: Given that: S=3-333,3-245,6-3106To express the the following matrices in the linear combination of…

Q: Q1) Consider the universal set U = {1,2, 3, 4, 5, 6, 7,8, 9} and sets A = (1,2,5, 6}, = {2,5, 7},C =…

A: Note: As per bartleby guidelines only first three sub parts are to be solved. Please upload other…

Q: 5. If X any Y are sets, then X-Y {r€X: z4Y} If X is open set and Y is closed set. Prove that (a) X-Y…

A: Let X is open set and Y is closed set