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In a class of 35 students, 24 like to pl...

In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football ?

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NCERT BANGLISH-SETS-MISCELLANEOUS EXERCISE ON CHAPTER 1
  1. In a class of 35 students, 24 like to play cricket and 16 like to play...

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

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

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

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

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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 A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some s...

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