Let A and B be sets. If `A nnX = B nnX =varphi`and `A uuX = B uuX`for – InterviewSolution

InterviewSolution

1.	Let A and B be sets. If `A nnX = B nnX =varphi`and `A uuX = B uuX`for some set X, show that `A = B`.(Hints `A = A nn(A uuX), B = B nn(B uuX)`and use Distributive law)
Answer» Let sets A and B are such that, for any set X, `A cupX=BcupX` `rArrAcap(A cupX)=A cap(BcupX)` `rArrAcap(A cupX)=(A cap B)cup (A cap X)` (From distributive law) `rArrAcap(A cupX)=(AcapB)cup phi(becauseA capX=phi)` `rArrA=(AcapB)cupphi` `rARr A =(A capB)`...(1) Again for any set X, `A cup X = B cup X` `rArr B cap (A cup X)=B cap (B cup X)` `rArr (B cup A)cup(B cap X)=B cap (B cup X)` (From distributive law) `rArr(B cupA)cup phi=Bcap(BcupX)[because(B capX)=phi]` `rArr(BcupA)cupphi=B` `rArr B=(B capA)` `rArr B= A cap B`....(2) From equations (1) and (2), `rArr A =B`.

Discussion

No Comment Found

Related InterviewSolutions

If A and B are two sets such that n (A ∪ B) = 50, n (A) = 28 and n (B) = 32, find n (A ∩ B).
The solution of `8x = 6 (mod 14)` isA. [8],[6]B. [8],[14]C. [6],[13]D. [8],[14],[16]
Find congruent solutions of `155-=7` (mod 4).
Find all congruent solutions of `8x -= 6` (mod 14).
Solve for X, if IX S 1. Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the value of m and n. respectively. can be the (f A and B be two sets containing 3 and 6 elements What
Two finite sets have m and n elements. The total number of subsets of first set is 56 more than the total number of subsets of the second set. Find the value of m and n.
Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are. (A) 7, 6 (B) 5, 1 (C) 6, 3 (D) 8, 7
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The value of m and n isA. 7, 6B. 6, 3C. 5, 1D. 8, 7
If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:(i) (A ∪ B)’ = A’ ∩ B’(ii) (A ∩ B)’ = A’ ∪ B’
Let A and B be sets. If A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X,show that A = B.(Hints A = A ∩ (A ∪ X), B = B ∩ (B ∪ X) and use distributive law)