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  • Let R be the relation on Z defined by R = {(a,b): a, b belongs to Z, a – b is an integer}. Find the domain and range of R.

Q9  Let R be the relation on Z defined by R = \left \{ ( a,b) : a , b \epsilon Z , a-b\: \: is \: \: an \: \: integer \right \}
      Find the domain and range of R.

Answers (1)

best_answer

It is given that
R = \left \{ ( a,b) : a , b \epsilon Z , a-b\: \: is \: \: an \: \: integer \right \}
Now, as we know that the difference between any two integers is always an integer.
And 
As Domain of R = set of all first elements of the order pairs in the relation.
Therefore,
 The domain of R = Z

Now,
Range of R = set of all second elements of the order pairs in the relation.
Therefore,
 range of R = Z

Therefore, the domain and range of R is Z and Z  respectively 

Posted by

Gautam harsolia

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