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2.Relations and Functions
medium
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 $4 ; x, y \in N \} .$ Depict this relationship using roster form. Write down the domain and the range.
Option A
Option B
Option C
Option D
Solution
$R=\{(x, y): y=x+5, x $ is a natural mumber less than $ 4, x, y \in N \}$
The natural numbers less than $4$ are $1,2,$ and $3 .$
$\therefore R=\{(1,6),(2,7),(3,8)\}$
The domain of $R$ is the set of all first elements of the ordered pairs in the relation.
$\therefore$ Domain of $R=\{1,2,3\}$ The range of $R$ is the set of all second
elements of the ordered pairs in the relation.
$\therefore$ Range of $R=\{6,7,8\}$
Standard 11
Mathematics
