Home
Class 11
MATHS
Let A and B be sets. If A nnX = B nnX =v...

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)

Text Solution

Verified by Experts

`A= A nn (A uu X)`
`= A nn (B uu X)`
`= (A nn B) uu (A nn X)`
`=(A nn B) uu phi` (by distributive law)
`A = Ann B` eqn(1)
now `B= B nn (B uu X)`
`= B nn (A uu X)`
`= (B nn A) uu (B nn X)`
...
Promotional Banner

Topper's Solved these Questions

  • SETS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|34 Videos

  • SETS

    NCERT ENGLISH|Exercise EXERCISE 1.3|9 Videos

  • SEQUENCES AND SERIES

    NCERT ENGLISH|Exercise EXERCISE 9.5|6 Videos

  • STATISTICS

    NCERT ENGLISH|Exercise EXERCISE 15.2|10 Videos

Similar Questions

Explore conceptually related problems

Let A and B be two sets that Acap X =Bcap X=phi and Acup X=Bcup X for some set X. then

Let A ,B and X be three sets such that A cap X= B cap X = phi and A cup X = B cup X .Then show that A=B .

For sets A, B,C , show that (A-B) cup (A-C) = A -(B cup C)

For all sets A and B, show that, A uu (B - A) = A uu B .

If A, B and C be sets. Then, show that A nn (B uu C) = (A nn B) uu (A nn C) .

Using properties of sets, show that (i) A uu ( A nn B) = A (ii) A nn (A uu B) =A .

Using properties of sets, show that(i) A uu( A nnB) = A (ii) A nn(Auu B) =A .

For any set A and B, show that (A-B)=(AnnB')

Let A , B and C be the sets such that A uu B=A uu C and A nn B = A nn C . show that B=C

Let A , B and C be the sets such that A uu B=A uu C and A nn B = A nn C . show that B=C