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: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: 6. The sets A and B are defined as: A = {2, 5, 7} B = {*, +} (a) Express the set A x B in roster…

A:

Q: Let A={3,6,9}, B={2,4,6,8}, C={ 1,2,3,4,5}and the universal set U={0,1,2,.,10}. Find each set (a)…

A:

Q: d) Give a recursive definition of the sequence {a„}, n = 1, 2, 3... %3D n if a,= 2 + 1; and a15 e)…

A: d)  Here, given that an=2+1=3 So, for all n, an=3 which is the recursive definition.

Q: Pzif akb then [a,b]-(- All of a,b are in real numbers

A: The given statements are: p: a<b q: a, b=(-∞, b] \ -∞, a Prove: If p, then q. If a<b, then  a,…

Q: Let A, B, and C be sets. Prove (AUB)NC= (ANC) U(BNC)

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Q: Show that each pair of sets is equivalent by using a one to one correspondence. {1,2,3,4,. . . .} is…

A:

Q: 6. Consider the following functions. [6T] f(x)=2x Determine the equation for h(x). Explain how you…

A: Given information:The graph of and To find: The function which is traced as the graph…

Q: True or false. The set S-{(-1,5), (3.–15)} spans R. false a) b) true O TRUE O FALSE Drouiour

A:

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: et A, B, C and D be sets. Prove that (AnB)u(CnD)=(AUC) n(BUC) n(AUD)n(BUD)

A: The set A∪B contains all the elements that are present either in set A or in set B. The set A∩B…

Q: If A and B are two sets prove that AUB=AUB

A: To prove that A complement union B complement is equal to the complement of the union of A and B .…

Q: Let A and B be subsets of some universal set U. Prove each of the following: *(a) An BCA * (b) A…

A:

Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

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: c) Let A and B be sets. Use properties of sets to show (A U B) n (A' O B)' = A

A: Given that                      A and B be sets. Then we have to show that…

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: Suppose A, B, C are sets. Prove that (AUB) – C = (A − C) U (B − C)

A: A∪B-C=A-C∪B-C

Q: For the universal set U {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y,…

A: Solution:     U – { a, b, c, d, e, f, g, h, i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x , y, z }…

Q: Prove. Power set of a null set is empty.

A:

Q: Q.No.2 Let X be a universal set and A, B be the subsets of X.Then prove the following. (a) ((A*…

A:

Q: Let U= {1, 2, …9} be the universal set and let A= {1, 2 , 3, 4, 5} and C= {5, 6, 7, 8, 9} and B= {1,…

A:

Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B)n (A × C)

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Q: Let A, B, C be sets. Prove A U (B and C) = (AUB) and (AUC)

A:

Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: Let 2 belongs to a set S. Now, consider the following definition if x belongs to S then (3x) belongs…

A: Given 2 belongs to set Sand given x belongs to S and then 3x belongs to S

Q: The difference of two sets, A - B, is defined as the set containing all elements of A except those…

A: U={1,2,3,4,5,6,7,8,9} A={3,5,9} B={2,4,6,7,8,9} A-B=A∩B' Therefore, first find B'=?

Q: 11. For sets A and B, define AAB=(A\B) U (B\A). (a) Let A and B be sets. Prove that A = B if and…

A: For sets  A and B , define                             A∆B=(A \ B)∪(B \ A) .  Then we have to show…