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If A sube B, prove that AxxA sube (A xxB...

If `A sube B`, prove that `AxxA sube (A xxB) nn (BxxA)`.

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If A sube B , prove that AxxC sube BxxC for any set C.

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

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

If A = A uu B , prove that B = A nn B .

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

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

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

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

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

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

MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. Let A be a non-empty set such that AxxB=AxxC. Show that B = C.

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  2. Prove that A sube B and C sube D imply : (A xxC) sube (B xxD).

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  3. If A sube B, prove that AxxA sube (A xxB) nn (BxxA).

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  4. If A sube B, prove that AxxC sube BxxC for any set C.

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  5. For any three sets A, B,C prove that : Axx (B uu C)= (AxxB) uu (AxxC)...

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

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  7. For any three sets A, B,C prove that : Axx (B uu C)= (AxxB) uu (AxxC)...

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

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

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  10. For any three sets A, B,C prove that : Axx(B^(c) uu C^(c))^(c)= (Axx...

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  11. For any three sets A, B,C prove that : Axx(B^(c) nn C^(c))^(c)= (AxxB...

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  12. State whether the following statement is true or false. If the stateme...

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  13. State whether the following statement is true or false. If the stateme...

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  14. State whether the following statement is true or false. If the stateme...

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  15. If A= {1, 2, 3} and B = {1, 2}, then find : AxxB.

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  16. If A= {1, 2, 3} and B = {1, 2}, then find : B xx A.

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  17. If A= {1, 2, 3} and B = {1, 2}, then find : Is AxxB= B xx A ?

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  18. If A= {1, 2, 3} and B = {1, 2}, then find : Represent AxxB graphically...

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  19. Let X = {- 2,0, 1}, Y = {2, 3}. Represent X xx Y and Y xx X graphicall...

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  20. Let A = {2, 3, 5, 7}, B = (1, 12, 13, 15}. How many elements are there...

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