4) Let {Aifier and {A;Jres be families of some non emppty sets such that Ai n Aj= A; NAj'= $ for all i, j E I with i #j. If A; A;' Vi€ I, +hen UA; ♡UAi'. Prove this! %3D

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: Use sets  U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},   A = {2, 4, 5, 7},  and  B = {1, 3, 4, 5, 6, 9, 10}…

A:

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: For the universal set U and the given sets U = {1,2,3,4,5,6,7,8,9,10}, A = {1,3,5}, B = {1,2},C =…

A:

Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: (a) Let A, B be sets. Prove that A\(An B) = A\B. You may assume all sets in the question are…

A:

Q: Prove by giving an example that if any set A, g. l. b(-A) = - l. u. b(A

A: Take a set A with two elements 1 and -1

Q: Consider following five sets: I.{ , } { } II. { } III. IV. { , , } V. { , } Find all set(s)…

A:

Q: Let R, S, T be subsets of the universal set U such that n(U) = 64, n(R U S U T) = 45, n(R) = 22,…

A: We will draw a Venn diagram using the given information: n(U) = 64, n(R U S U T) = 45, n(R) = 22,…

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

A:

Q: Let A, B and C be sets. Prove that  A ⊆ C and B ⊆ C, then A ∪ B ⊆ C

A:

Q: Let {Aa: a E I} be an indexed family of sets and let B be a set. Prove: (Uael Aa) nB = Uael( Aan B)

A:

Q: 2. Let A = {0,2,4,6,8} and B = {1,3,5,7} have universal set U = {0,1,2,…..,8}. Find: (a) Ā (b) В (d)…

A: 2. Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…