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Let R be the relation on Z defined by R = { ( a , b ) } : € Z , a - b is an integer. ) Find the domain and range of R ?
Most Upvoted Answer
Let R be the relation on Z defined by R = { ( a , b ) } : € Z , a - b ...
The relation R on Z is defined by 


R={(a,b):a,b∈Z,a−b is an integer}


Since a−b is an integer for all a, b∈Z. 


So, Domain (R)=Z, Range (R)=Z.
Community Answer
Let R be the relation on Z defined by R = { ( a , b ) } : € Z , a - b ...
Note that [.] is greatest integer function and {.} is fractional part function. We know that for any number,
x = [x] + {x}
=> x - {x} = [x]
Since [x] is always an integer x - {x} will always be an integer.
If a = x is any real number then we must define b = {x} for a - b to be an integer.
So, the domain of (a,b) is (x,{x}) and is range is Z (all integers).
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Let R be the relation on Z defined by R = { ( a , b ) } : € Z , a - b is an integer. ) Find the domain and range of R ?
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Let R be the relation on Z defined by R = { ( a , b ) } : € Z , a - b is an integer. ) Find the domain and range of R ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Let R be the relation on Z defined by R = { ( a , b ) } : € Z , a - b is an integer. ) Find the domain and range of R ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the relation on Z defined by R = { ( a , b ) } : € Z , a - b is an integer. ) Find the domain and range of R ?.
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