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(i) If A sube B, prove that A xx A sube ...

(i) If `A sube B`, prove that `A xx A sube (A xx B) nn (B xx A)`
(ii) If `A sube B`, prove that `A xx C sube B xx C` for any set C.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Exercise-2(a)
  1. If R is the set of all real numbers, what do the cartesian products R...

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  2. If A= [a,b,c], B= [c,d] and C= [d,e,f], Find (i) A xx (B uu C) (ii) ...

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  3. (a) Let A= {1,2,3}, B= [3,4] and C={4,5,6}. Find: (i) (A xx B) nn (A...

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  4. Let A= {(1)/(2), 2}, B= [2,3,5], C= {-1, -2}. Verify that A xx (B nn C...

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  5. Let A = {1,2,3}, B = {2,3,4} and C= {4,5). Verify that: A xx (B uu C...

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  6. If A = [1,2,3], B=[4], C= [5], then verify that: (i) A xx (B uu C) =...

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  7. Let A= [1,2,3], B = [-1,0,1,2,3], C= {1}, D= {-1,1}. Then verify the f...

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

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  9. Theorem 3 (If A and B are two non empty set; then prove that AxxB=BxxA...

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

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  11. If A sube B and C sube D, then prove that: A xx C sube B xx D

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  12. (i) If A sube B, prove that A xx A sube (A xx B) nn (B xx A) (ii) If...

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  13. Theorem 1(i) (For any three set A;B;C; prove that Axx(BuuC)=(AxxB)uu(A...

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  14. For any three sets A, B and C, prove that: (A -B) xx C= (A xx C) - (...

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  15. For any A sets A, B, C and D, prove that: (AxxB) nn (CxxD)=(A nnC)xx...

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  16. For any three sets A ,B ,C prove that: Axx(B^(prime)uuC^(prime))^'=(A...

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  17. If A= {1,2,3} and B={1,2}, then find: (i) A xx B (ii) B xx A (iii)...

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  18. Let X= (-2,0,1), Y = {2,3}. Reprsent X xx Y and Y xx X graphically. ...

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

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  20. Theorem 9(A and B are two non empty set having n element in common ; t...

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