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Decide, among the following sets, which ...

Decide, among the following sets, which sets are subsets of one and another:
A = { `x : x ∈ R and x` satisfy `x^(2) – 8x + 12 = 0` },
`B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }`.

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The correct Answer is:
`A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B, D ⊂ C`
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NCERT BANGLISH-SETS-MISCELLANEOUS EXERCISE ON CHAPTER 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. Show that the following four conditions are equivalent : A ⊂ B

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

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

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

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

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

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

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

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

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

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

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

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