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# Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural number less than 4; x, y belongs to N}. Depict this relationship using roster form. Write down the domain and the range.

Q2  Define a relation R on the set N of natural numbers by $R = \left \{ ( x,y ) : y = x +5 , x$ is a natural number less than $4 ; x , y \epsilon N \left. \right \}$. Depict this relationship using roster form. Write down the domain and the range.

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It is given that
$R = \left \{ ( x,y ) : y = x +5 , x$ is a natural number less than $4 ; x , y \epsilon N \left. \right \}$

As x is a natural number which is less than 4.
Therefore,
the relation in roaster form is,  $R = \left \{ (1,6), (2,7), (3,8) \right \}$
As Domain of R = set of all first elements of the order pairs in the relation.
Therefore,
Domain of   $R = \left \{ 1, 2, 3 \right \}$

Now,
Range of R = set of all second elements of the order pairs in the relation.
Therefore,
the range of   $R = \left \{ 6, 7, 8 \right \}$

Therefore,  domain and the range are $\left \{ 1,2,3 \right \} \ \ and \ \ \left \{ 6, 7, 8 \right \}$  respectively

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