Home
Class 11
MATHS
Let A, B and C be the sets such that A ...

Let A, B and C be the sets such that `A uuB = A uuC`and `A nnB = A nnC`. Show that `B = C`.

Text Solution

Verified by Experts

(i) `because` Sets A, B and C are such that
`A cup B = A cup C`
or `(A cup B) cap B = (A cupC) cap B`
or `(A cap B) cup (B cap B) = (A cap B) cup (C cap B)` (From distributive law)
or `B = (A cap B) cup (C cap B)` ….(1)
[Since `(A cap B) cup (B cap B)=B`]
Again `(A cup B) = (A cup C)`
or `(A cup B) cap C = (A cup C) cap C`
or `(A cap C) cup (B cap C)= (A cap C) cup (C cap C)` [From distributive law)
or `(A cap C) cup (B cap C) = C` [Since `(A cap B) cup (C cap C)=C`]
then `C = (A cap C) cup (B cup C)`...(2)
`because` Given `A cap B = A capC` then, replace `(A cap C)` by `(A cap B)` in equation (2),
`C = (A cap B) cup (B cup C)`...(3)
Now comparing equation (1) and equation (3),
`B=C`.
Promotional Banner

Topper's Solved these Questions

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.6|8 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|32 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|7 Videos

Similar Questions

Explore conceptually related problems

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

If A, B and C are three sets such that A cup B = A cup C and A cap B = A cap C , then prove that B = C .

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

Let A and B be two sets such that n (A) = 52, n (B) = 60 and n(A nn B) = 16. Draw a Venn diagram and find n(A uuB )

Show that A nnB = A uuB implies A = B

If A and B are two sets then prove that (AuuB)'uu(A'nnB)=A'

Three sets A,B and C are such that A=B nnC and B=CnnA

Find sets A, B and C such that A nnB , B nnC and A nnC are nonempty sets and A nnB nnC=varphi .

Find sets A, B and C such that A nnB , B nnC and A nnC are nonempty sets and A nnB nnC=varphi .