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If A={1,2,3},B={4},C={5}, then verify th...

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

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Given` A={1,2,3},B={4},C={5}`
So`,(B uu C)={4,5}`
`A xx (B uu C)={(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)}`
`(Axx B)={(1,4),(2,4),(2,5)}`
`(A xx C)={(1,5),(2,5),(3,5)}`
`(A xx B) uu (Axx C)={(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)}`
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Findxa n dy , if (x+3,5)=(6,2x+y)dot

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  2. If A={a ,b} and B={1,2,3}, find AxxB ,BxxA and (AxxB)nn(BxxA)

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

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  4. A relation R is defined from a set A={2,3,4,5} to a set B=3,6,7,10 as ...

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

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

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

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

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  9. Let R be the relation on the set N of natural numbers defined by R={(a...

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  10. If R is the relation "less than" from A={1,2,3,4,5} to B={1,4,5}, writ...

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  11. A relation R is defined on the set Z of integers as: (x ,y) in R x^2...

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  12. For the relation R1 defined on R by the rule (a ,b) in R1:1+ab >...

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  13. Find the values of a\ a n d\ b ,\ if\ (3a-2,\ b+3)=(2a-1,\ 3)dot

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

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  15. If A={1,2,3},\ B={3,4}a n d\ C={1,3,5} , find Axx(BuuC)

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  16. If A={1,2,3},\ B={3,4}a n d\ C={1,3,5} , find Axx(BnnC)

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  17. If A={1,2,3},\ B={3,4}a n d\ C={1,3,5} , find (AxxB)nn(AxxC)

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  18. If A={1,2},\ from the set AxxAxxA

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  19. If R is the set of all real numbers, what do the cartesian products R...

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  20. Let A and B be two sets such that AxxB consists of 6 elements. If thre...

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