Question

Suppose that 120 students are studying in 4 sections of eleventh standard in a school. Let A denote the set of students and B denote the set of the sections. Define a relation from A to B as “x related to y if the student x belongs to the section y”. Is this relation a function? What can you say about the inverse relation? Explain your answer

Answer 1

Given: A denotes the set of students and B denotes the set of sections.

Also given there 120 students and 4 sections.

Let f be a relation from A to B as “x related to y if the student x belongs to the section y”

Two are more students in A may belong to same section in B.

But one student in A cannot belong to two or more sections in B.

Every student in A can belong to any one of the section in B.

Therefore / is a function.

In B we can have sections without students.

Every element in B need not have preimage in A.

∴ f need not be onto.

Thus, f is a function and inverse relation for f need not exist.