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Theorem 9(A and B are two non empty set ...

Theorem 9(A and B are two non empty set having n element in common ; then prove that `AxxB` and `BxxA` have `n^2` element in common.)

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Let,A has `x` elements and B has y elements in total.
Their cartesian product` AxxB` will have `x×y` elements
Hence if they have n elements in common. `n^2` common elements are present in the products` AxxB` and `BxxA`
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. For any sets A ,B ,C ,D prove that: (AxxB)nn(CxxD)=(AnnC)xx(BnnD)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Let A and B be two sets such that n(A)=5\ a n d\ n(B)=2,\ if\ a ,\ b ,...

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  18. If (a/3-1,\ b-1/3)=(5/3,2/3) , find the values of a\ a n d\ bdot

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  19. If the ordered pairs (x ,-1) and (5, y) belong to the set {(a , b): b=...

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  20. If (x+1,\ 1)=(3,\ y-2), find the value of x and y.

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