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: Question 3  Show that if A and B are sets with A ⊆ B, then A ∩ B = B.  Full explain this question…

A: Show that if A and B are sets with A ⊆ B, then A ∩ B = 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: 11.0, Prove that the interior of the interin of a set is equal to the interies of that set

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Q: For all sets A B and c, of CAXC)- CBrC)# Ø, then A-B#¢.

A:

Q: |x²| = p^ n

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

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

A:

Q: 4) Let {AifieI and {Aí Jies be families of some non empty sets such that A; MA;= A₁ NA; = for all ₁₁…

A: Let, x∈∪i∈IAi So, for some i∈I, there exists some Ai such that x∈Ai Now, given that Ai≈Ai' for all…

Q: Find the following sets: U= { 1,2,3,4,5} A ={1,2,3} B={5} 11. A’                             16. B’…

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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 relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

A: We know that

Q: Let U = {a,b,c,d,e,f, 12, 13, 14, 15, 16, 17), X = {a,b,c,13,14,15), and Y = {b,d,f, 12,14,16}. List…

A:

Q: 2. Let U = {0,1,2,3,4,5,6,7,8,9,10); a) How many subsets will A have? b) Lis only the elements of…

A: as per Bartleyby rules we have to answer only 3 subparts.

Q: nsider the sets A = {1, 2} and B = {3,4}. Verify that, for these sets, the following iden d: 1.…

A:

Q: Consider the following sets: A = {1, 2, 3} and B = {2, 3, 4}. Determine the cardinality of the set…

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Q: Sets B and C are subsets of the universal set U. These sets are defined as follows. U={f,k,m, x,y }…

A: It is given that: U=f,k,m,x,y,B=k,y,C=f,k,m Therefore the complementary sets of B and C are:…

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

A:

Q: (1) In the universal set U ={1,2,3,4,5} we define the following sets: A ={1,2,3}, B = {3,4}, and C =…

A: Note: You have posted a question with multiple subparts. We have solved the first three subparts for…

Q: 4) Let (AilieI and {Ai lies be families of some non empty sets such that A; NA;= ANA;' = for all i,…

A: It is given that,  Aii∈I and A'ii∈I be the families of some non empty sets such that ;   Ai∩Aj =…

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

A:

Q: X, Y and Z be subsets of the set . Verify the following properties: XCY XUY=Y⇒XnY=X -UI 3)

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Q: Let U = {a,b,c,d,e,f,17,18,19,20,21,22}, List the members of the set X'nY', using set braces. X =…

A:

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…

A:

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: Given the sets A= {1, 2, 3), B = {0, 1, 2, 3,...), and C= {0, 1, 2}, tell which of the following…

A: For three given set A, B, C we have to check which sets are subsets of the other sets.

Q: Let A, B, and C are three sets, prove that B×(AnC)=(B× A)^(B×C)

A: Given 3 sets A, B and C. We have to prove that B×A∩C=B×A∩B×C. For this, we have to show that…