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Let R be the relation on Z defined by R=...

Let `R` be the relation on `Z` defined by `R={(a , b): a , b in , a-b` is an integer`}dot` Find the domain and range of `Rdot`

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Given R={(a,b):a,b∈Z,a−b is an integer}
a∈Z So, Domain of R is Z.
R is such that a−b∈Z and we have a∈Z so b∈Z.
So, Range of R is Z.
∴ Domain of R=Z and Range of R=Z.
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Knowledge Check

  • Let R be the relation on Z defined by R = P(a,b) : a,b in Z , a-b is an integers}. then

    A
    domain of R is {2,3,4,5,.....}
    B
    range of R is Z
    C
    Both (1) and (2)
    D
    None of the above

  • Let R={(a,b) :a,b in N and b=a+5,a lt4}. find the domain and range of R.

    A
    domain `( R)={1,2,3}` and range `( R) ={6,2,8}`
    B
    domain `( R)={1,2,3}` and range `( R) ={6,7}`
    C
    domain `( R)={1,2,3}` and range `( R) ={6,7,8}`
    D
    domain `( R)={2,3}` and range `( R) ={6,7,8}`
    • RD SHARMA-RELATIONS-Solved Examples And Exercises
    1. Let R be the relation on Z defined by R={(a , b): a , b in , a-b is a...

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    2. If A={1,2,4},B={2,4,5},C={2,5},t h e n(A-B)xx(B-C) is (a){(1, 2), (1...

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    3. If Aa n dB are two sets having 3 elements in common. If n(A)=5,n(B)=4,...

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    4. If A={1,3,5},B={x ,y} find the following products AxxB (ii) BxxA (iii...

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

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

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

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

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

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    10. If AsubeB , and CsubeD , prove that AxxCsubeBxxDdot

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

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

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

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

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

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

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

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

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

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