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In each of the following, determine whet...

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If `A ⊂ B and x ∉ B` , then `x ∉ A`

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NCERT BANGLISH-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. In each of the following, determine whether the statement is true or f...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some s...

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  17. Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty s...

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

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

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

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