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Let A={-1,3,5} and B={2,3} find the fol...

Let `A={-1,3,5}` and `B={2,3}` find the following products (i) `AxxB` (ii) B`xxA` (iii) `AxxA`

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Given`,A={−1,3,5} and B={2,3}`
`A xx B={(-1,2),(-1,3),(3,2),(3,3),(5,2),(5,3)}`
`B xx A={(2,-1),(2,3),(2,5),(3,-1),(3,3),(3,5)}`
`A xx A={(-1,-1),(-1,3),(-1,5),(3,-1),(3,3),(3,5),(5,-1),(5,3),(5,5)}`
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let R be a relation in N defined by (x ,y) in R x+2y=8 . Express Ra ...

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

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  3. Let A={-1,3,5} and B={2,3} find the following products (i) AxxB (ii) ...

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

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

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

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

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  8. If A={1,2},B={3,4}a n dC={4,5,6}dotT h e n , AxxB={1,2}xx{3,4}={(1,3)...

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  9. Findxa n dy , if (x+3,5)=(6,2x+y)dot

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

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

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

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

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

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

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

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

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

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

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