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

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

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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: 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: 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: 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: 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