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Prove the following : A sub B iff A^(c) ...

Prove the following : `A sub B iff A^(c) sup B^(c)`.

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Prove the following : B-A=B nn A^(c) .

Prove that following : (A uu B=U) iff B^(c) sub A iff A^(c) sub B .

Prove the following : B sub A implies A uu B=A .

Let A = {1, 2, 3}, B= {- 1,0, 1,2,3} and C= {1}, D={- 1,1}. Then Verify the following : If A sub B and C sub D , then (A xxC) sub (BxxD) .

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MODERN PUBLICATION-SETS-EXERCISE
  1. If A = {1, 2, 3, 4, 5}, B = {2, 3,5, 7, 9} and C = {3, 4, 6, 8, 10}, t...

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  2. Prove that A sub B,B sub C implies A sub C.

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  3. Prove the following : A sub B iff A^(c) sup B^(c).

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  4. Prove the following : A sub B iff A nn B=A.

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  5. Prove the following : A sub B iff A uu B=B.

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  6. Prove that following : (x notin A implies x notin B) iff B sub A .

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  7. Prove that following : (A uu B=U) iff B^(c) sub A iff A^(c) sub B.

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  8. Prove that following : (A nn B=phi) iff A sub B^(c) implies B sub A^(...

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  9. Prove the following : B-A=B nn A^(c).

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  10. Prove the following : (A uu B)-A=B-A .

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  11. For sets A,B and C, prove that : A-(B-C)=(A-B) uu(A nn C).

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  12. For sets A,B and C, prove that : A-(B uu C)=(A-B) nn (A-C).

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  13. If A, B and C are any three sets, then prove that : A nn (B-C) = (A nn...

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  14. If A, B and C are any three sets, then prove that : A nn (B-C) = (A nn...

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  15. For sets A,B and C, prove that : (A-B)nn C=(A nn C)-B.

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  16. If A and B are subsets of the universal set U, then show that : B su...

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  17. If A and B are subsets of the universal set U, then show that : (A n...

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  18. If A and B are subsets of the universal set U, then show that : (A n...

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  19. Using properties of sets, show that A uu ( A nn B)=A

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  20. Using properties of sets, show that A nn (A uu B)=A

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