Home
Class 11
MATHS
If A and B are two sets, then prove that...

If A and B are two sets, then prove that the sets A - B, B - A and `A cap B` are mutually disjoint.

Text Solution

Verified by Experts

`A - B={x:x in A and x in B}`
`B-A={x:x in B and x in A}`
` : A- B and B -A` are mutually disjoint
Now, `x in A - B rArr x in A and x in B`
`rArr x cancel(in) A cap B`
`:. A- B and A cap B` are mutually disjoint.
Similarly, we can prove that `B - A adn A cap B` are mutually disjoint
Therefore, `A - B, B-A and A cap B` are mutually disjoint sets.
Promotional Banner

Topper's Solved these Questions

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1A|7 Videos

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1B|10 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

If A and B are any two sets, then

If A and B are two sets, then prove that A^(c )-B^(c )=B-A .

If A and B are two sets prove that Ann(B-A)=phi

If A and B are two sets then prove A = A nn(A uu B).

If A and B are any two sets, then prove that (A nn B) uu (A-B)=A

If A and B are two sets, then prove that : A cupB=A capBhArrA=B .

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

If A and B are any sets, prove that Ann(B-A)=phi

if A and B are two sets, then prove that, (A cup B)' cup (A' cap B) = A' .

If A and B are two sets, then A nn (A uu B) equals