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For any sets A and B, show that P ( A ...

For any sets A and B, show that
`P ( A ∩ B ) = P ( A ) ∩ P ( B )`.

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NCERT TAMIL-SETS-MISCELLANEOUS EXERCISE ON CHAPTER 1
  1. For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ).

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  2. Decide, among the following sets, which sets are subsets of one and a...

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  3. Determine whether the statement is true or false. If it is true, prove...

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  4. In each of the following, determine whether the statement is true or f...

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  5. Determine whether the statement is true or false. If it is true, prove...

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  6. In each of the following, determine whether the statement is true or f...

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  7. In each of the following, determine whether the statement is true or f...

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  8. In each of the following, determine whether the statement is true or f...

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

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

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

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

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

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

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

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

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

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

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

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

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

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