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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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i)L.H.S=`Axx(B^(prime)uuC^(prime))^'`
=`Axx((B^(prime))'nn(C^(prime))')`
=`Axx(BnnC)`
=`(AxxB)nn(A xx C)`
so,L.H.S=R.H.S
ii)L.H.S=`Axx(B^(prime)nnC^(prime))^'`
=`Axx((B^(prime))'uu(C^(prime))')`
=`Axx(BuuC)`
...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. If A={1,2} , find AxxAxxAdot

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  2. Theorem 2 (For any three set A;B;C; prove that Axx(B-C)=(AxxB)-(AxxC)

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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 BsubeA , show that BxxBsube(AxxB)nn(BxxA)dot

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  5. If Aa n dB are any two non-empty sets, then prove that: AxxB=BxxA A=B...

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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 Cdot

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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, x ...

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

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

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

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

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

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

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

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

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

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