Home
Class 11
MATHS
Show that A nn B=A nn C need not imply B...

Show that `A nn B=A nn C` need not imply `B=C`

Text Solution

Verified by Experts

Let A,B and C are three sets such that
`A = {a,b},B={b,c}`
and `C = {b,d}`
Here `A cap B = {a,b} cap {b,c} ={b}`
and `A cap C = {a,b}cap {b,d} = {b}`
Therefore, `A cap B = {b} = A cap C`
but we see that `B ne C`
Therefore, `A cap B = A cap C` need not imply `B = C`.
Promotional Banner

Topper's Solved these Questions

  • SETS

    NAGEEN PRAKASHAN|Exercise Exercise 1.6|8 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|32 Videos

  • STATISTICS

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|7 Videos

Similar Questions

Explore conceptually related problems

Show that AcapB=AcapC need not imply B=C.

Show that A nn B=A nn B implies A=B

Find sets A,B and C such that A nn B,B nn C and A nn C are non empty sets and A nn B nn C=phi

Prove that A-B=A nn B^(c)

If A, B and C are three sets such that A nn B = A nn C and AuuB = A uu C , then

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

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 sets such that A nn B sube C and A nn B!=phi. Then which of the following statements is not true?

The probabilities of three events A,B,C are such that P(A)=0.3, P(B)=0.4, P(C)=0.8,P(A nn B)=0.09, P(Ann C) = 0.28, P(A nn B nn C) 0.08 and P(Auu B uu C) leq 0.75.Show that P(B nn C) lies in the interval [0.21, 0.46].