Question

Let A be the set of all 50 students of Class X in a school. Let f : A → N befunction defined by f(x) = roll number of the student x. Show that f is one-onebut not onto​

Answer 1

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Solution 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 ofstudents are from 1 to 50. This implies that 51 in N is not roll number of any student ofthe class, so that 51 can not be image of any element of X under f. Hence, f is not onto.