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Let A = {1, 2, 3}, B= {- 1,0, 1,2,3} and...

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-RELATIONS AND FUNCTIONS -EXERCISE
  1. Let A= {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} andD = {5, 6, 7, 8}. Verif...

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  2. Let A = {1, 2, 3}, B= {- 1,0, 1,2,3} and C= {1}, D={- 1,1}. Then Verif...

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  3. Let A = {1, 2, 3}, B= {- 1,0, 1,2,3} and C= {1}, D={- 1,1}. Then Verif...

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  4. Let P = {1, 4,9} and Q= {2,4,6}. Write the elements of (P nn Q)xx (P u...

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  5. IfA and B are non-empty sets and A xx B=B xx A, then

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  6. Let A be a non-empty set such that AxxB=AxxC. Show that B = C.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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