4) Let {AifieI and {Aí Jies be families of some non empty sets such that A; MA;= A₁ NA; = for all ₁₁ JEI with i#j. If A; A VIEI, then UA; ~UA. Prove this! ¡EI ¡GI

Q: Which of the following set is consistent? Select one: O i. None of these O i. (A&~(BVA)} O i. (/ ) >…

A: Option 4 ) { A ⊃ B , B ⊃ C , A ⊃ C }  is correct

Q: Let T be the set of all TSU students. Determine if (T, R) a poset or not if R = {(a, b)|a ∈ T, b ∈…

A: 1 We  List all of the ordered pairs in the relation R = {(a, b)|a + b is even} on the set {1, 2, 3,…

Q: a) Suppose A is a finite set and B is any set. Show that |A| = |A\ B| + |A n B|. (Hint: Use Theorem…

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

A:

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

A: Given: A, B and C are sets. To show: a) What we need to prove show to prove the following using…

Q: 4) Let {Aifier and {A;Jres be families of some non emppty sets such that Ai n Aj= A; NAj'= $ for all…

A:

Q: Question:- let V be the set f all oldeled paits 7 Yeal number. Check whether V is a veeter spare…

A: Axioms of vector space V Let x, y, z∈V and a, b∈R 1) Addition: (a) x+y=y+x (b) (x+y)+z=x+(y+z) (c)…

Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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: B. Let B and C be the subsets of some universal set X, then prove that (C – B)' = BU C'

A: let B and C be the subsets of some universet x1 then prove that (c-B)' = BUC'

Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

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

A:

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

A:

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Assume all sets are subsets of a universal set U. Suppose that A, B, and C are arbitrary sets, Prove…

A: Given, A-C∪B-C=A-Bc∪C

Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

A:

Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: 3. (10 points) a) Use an element proof to prove the following: for all sets A and B, A - (ANB) = A –…

A: The detailed solution is as follows below:

Q: (a) For any sets A, B and C, prove that if AC BUC and AnC= Ø, then ACB.

A: Since you have posted multiple questions according to guidelines we can solve only first question.…

Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

A:

Q: Suppose that A and B are finite sets. Prove that AxB is finite.

A: Result 1 :  A be an non-empty finite set if and only if cardinality of A is a finite natural number…