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For any sets A and B, prove that : P (A ...

For any sets A and B, prove that : `P (A nn B) =P (A) nn P (B)`.

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For any three sets A, B,C prove that : (A nn B) xx C= (AxxC) nn (BxxC) .

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For any four sets A, B, C and D, prove that : (A nn B)xx (C nn D)= (AxxC) nn (BxxD) .

For any two sets A and B, prove that : A Delta B= (A uu B)- (A nn B) .

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

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

Prove that : A nn(B-A)=phi .

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

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MODERN PUBLICATION-SETS-EXERCISE
  1. Let A and B be two sets. Prove that : (A -B) uu B= A if and only if B ...

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  2. Prove that if A uu B=C and A nn B=phi, then A= C-B.

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  3. For any sets A and B, prove that : P (A nn B) =P (A) nn P (B).

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  4. Show that for any sets A and B, A = ( A nn B) uu ( A -B ) and A uu (B-...

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

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

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  7. Show that A nn B = A nn C need not imply B = C.

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  8. Prove that if a set has only one clement then it has 2 subsets.

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  9. Prove that If B sub A and if B has one element less than that of A, pr...

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  10. Deduce from these two results that a set with 2 elements has 2^2 subse...

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  11. Prove that A^c-B^c=B-A.

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  12. Draw appropriate Venn diagram for the following : (A uu B)'

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  13. Draw appropriate Venn diagram for the following : A' nn B'

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  14. Draw appropriate Venn diagram for the following : (A nn B)'

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  15. Draw appropriate Venn diagram for the following : A' uu B'

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  16. Prove that : (A uu B uu C)^(c) =A^(c) nn B^(c) nn C^(c).

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  17. If A = {1, 2, 3}, B= { 4, 5, 6} and C= { 7, 8, 9}, verify that : A ...

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  18. Prove that : (A uu B)=(A-B) uu (B-A) uu (A nn B).

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  19. For any two sets A and B, prove that : A Delta B= (A uu B)- (A nn B).

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  20. For any two sets A and B, prove that : (A-B) uu (B-A) = (A uu B)- (A n...

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