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Theorem 2 (For any three set A;B;C; prov...

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

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Given,`=>(x,y) in Axx(B-C)----(i)`
`=>x in A and y in (B-C)`
`=>x in A and [y in B and y !in C]`
`=>x in A and y in B and x in A and y !in C`
`=>(x,y) in (A,B) but (x,y) !in (A,C)`
`=>(x,y)in (AxxB)-(Bxxc)----(ii)`
Thus,
From (i) and (ii),
...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. If A={1,3,5},B={x ,y} find the following products AxxB (ii) BxxA (iii...

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  2. If A={1,2} , find AxxAxxAdot

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

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

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  5. If BsubeA , show that BxxBsube(AxxB)nn(BxxA)dot

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

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  7. If AsubeB , and CsubeD , prove that AxxCsubeBxxDdot

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  8. If AsubeB , prove that AxxCsubeBxxC for any set Cdot

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

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

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

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

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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 the following products (i) AxxB (ii) ...

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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 AxxBa...

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

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