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Prove that If B sub A and if B has one e...

Prove that If `B sub A` and if B has one element less than that of A, prove that A has twice as many subsets as B.

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MODERN PUBLICATION-SETS-EXERCISE
  1. Show that A nn B = A nn C need not imply B = C.

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Let A = {1, 2, 3, 4,5}, B = {2, 3, 5, 7} and C = {1, 2, 4, 6} be the s...

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  16. Let A = {1, 2, 3, 4,5}, B = {2, 3, 5, 7} and C = {1, 2, 4, 6} be the s...

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  17. Let A = {1, 2, 3, 4,5}, B = {2, 3, 5, 7} and C = {1, 2, 4, 6} be the s...

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  18. Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, the Auu(BnnC) is

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  19. If A = {0, 1, 2, 3, 5,6}, B = {1,3, 5, 7, 9} and C = {0, 5, 10, 20,40}...

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  20. Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, the Auu(BnnC) is

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