Let $A$ be the set of all $50$ students of Class $X$ in a school. Let $f: A \rightarrow N$ be function defined by $f(x)=$ roll number of the student $x$. Show that $f$ is one-one but not onto.
Let $A$ be the set of all $50$ students of Class $X$ in a school. Let $f: A \rightarrow N$ be function defined by $f(x)=$ roll number of the student $x$. Show that $f$ is one-one but not onto.
No two different students of the class can have same roll number. Therefore, $f$ must be one-one. We can assume without any loss of generality that roll numbers of students are from $1$ to $50 .$ This implies that $51$ in $N$ is not roll number of any student of the class, so that $51$ can not be image of any element of $X$ under $f$. Hence, $f$ is not onto.
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