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Let A and B be sets. If AcapX=BcapX=phi ...

Let A and B be sets. If A`cap`X=B`cap`X=`phi` and A`cup`X=B`cup`X for some set X, show that A=B.
(Hints A=A`cap`(A`cup`X), B=B`cap`(B`cup`X) and use distributive law)

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NCERT TAMIL-SETS-MISCELLANEOUS EXERCISE ON CHAPTER 1
  1. In each of the following, determine whether the statement is true or f...

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  2. Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C....

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  3. Show that the following four conditions are equivalent : A ⊂ B

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  4. Show that the following four conditions are equivalent : A – B = φ

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  5. Show that the following four conditions are equivalent : A ∪ B = B

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  6. Show that the following four conditions are equivalent : A ∩ B = A

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  7. Show that if A ⊂ B, then C – B ⊂ C – A.

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  8. Assume that P ( A ) = P ( B ). Show that A = B

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  9. Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )?...

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  10. Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ...

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  11. Using properties of sets, show that A ∪ ( A ∩ B ) = A

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  12. Using properties of sets, show that A ∩ ( A ∪ B ) = A.

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  13. Show that A ∩ B = A ∩ C need not imply B = C.

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  14. Let A and B be sets. If AcapX=BcapX=phi and AcupX=BcupX for some set X...

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  15. Find sets A, B and C such that AcapB, BcapC and AcapC are non-empty se...

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  16. In a survey of 600 students in a school, 150 students were found to be...

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  17. In a group of students, 100 students know Hindi, 50 know English and 2...

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  18. In a survey of 60 people, it was found that 25 people read newspaper H...

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  19. In a survey of 60 people, it was found that 25 people read newspaper H...

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  20. In a survey it was found that 21 people liked product A, 26 liked prod...

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