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For any three sets `A ,B ,C` prove that: `Axx(B^(prime)uuC^(prime))^'=(AxxB)nn(AxxC)` and `Axx(B^(prime)nnC^(prime))^'=(AxxB)uu(AxxC)`

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For any three sets A ,B ,C prove that: Axx(B^(prime)uuC^(prime))^'=(AxxB)nn(AxxC) Axx(B^(prime)nnC^(prime))^'=(AxxB)uu(AxxC)

For any two sets of A and B, prove that: B^(prime)uuA '=>AsubB

For any two sets of A and B, prove that: A^(prime)uuB=U=>AsubB

For any sets A ,B ,C ,D prove that: (AxxB)nn(CxxD)=(AnnC)xx(BnnD)

For any two sets A\ a n d\ B , prove that AnnB=varphi=>AsubeB^(prime)dot

For any two sets A and B prove the following: Ann(A^(prime)uuB)=AnnB

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

Axx(B-C)=(AxxB)-(BxxC)

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x^2+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

If A={1,2,3},B={4},C={5}, then verify that: Axx(BuuC)=(AxxB)uu(AxxC)

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let Aa n dB be two sets. Show that the sets AxxB a n dBxxA have an ele...

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  2. If A={1,5} , B={3} , find AxxB

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

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  4. If AsubeB , show that AxxAsube(AxxB)nn(BxxA)dot

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  5. If A and B are any two non-empty sets, then prove that: AxxB=BxxA ' im...

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  6. If AsubeB , and CsubeD , prove that AxxCsubeBxxDdot

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  7. If AsubeB , prove that AxxCsubeBxxC for any set C.

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  8. If R is a relation on the set A={1,2,3,4,5,6,7,8,9} given by x R y⇔y =...

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  9. If A={1,2,3},B={4,5,6}, which of the following are relations from AtoB...

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  10. A" "=" "{1," "2," "3." "5}" "a n d" "B" "=" "{4," "6," "9} . Define a ...

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  11. Let R be the relation on the Z of all integers defined by (x ,y) in R...

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  12. A relation R is defined from {2,3,4,5} to{3, 6, 7, 10}by : x R y :x i...

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  13. Let R be a relation in N defined by (x ,y) in R x+2y=8 . Express R a...

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  14. The Cartesian product A xxA has 9 elements among which are found (...

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  15. Let A={-1,3,5} and B={2,3} find AxxB

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  16. Express A={(a ,b):2a+b=5,a ,b in W} as the set ordered pairs.

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  17. If AxxB={(a ,1)(b ,3),(a ,3),(b ,1),(a ,2),(b ,2)}, find Aa n dBdot

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  18. Let A={1,2,3}and B={x : x in N ,x is prime less than 5}. Find AxxB

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  19. If AxxB={(a ,1)(a ,5),(a ,2),(b ,2),(b ,5),(b ,1)}, find BxxAdot

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  20. If A={1,2},B={3,4} find AxxB

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