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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 B ∈ C` , then `A ∈ C`

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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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KUMAR PRAKASHAN-SETS-MISCELLANEOUS EXERCISE : 1
  1. Decide, among the following sets, which sets are subsets of one and a...

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

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  9. A is the set of prime number less than 10, B is the set of odd numbers...

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

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

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

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

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

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

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

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

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

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

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

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