Question

Let \( R \) be a relation defined by \( R = \{(x, y) : x, y \text{ are Roll Numbers of students such that } y = x^3 \} \). List the elements of \( R \). Is \( R \) a function? Justify your answer.

Hint:

A relation is a function if for each element in the domain, there is exactly one corresponding element in the codomain.

Answer 1

The relation \( R \) comprises pairs where the second roll number is the cube of the first. For the roll numbers \( 1, 2, 3, 4, 5 \), the elements of \( R \) are: \[ R = \{ (1, 1), (2, 8), (3, 27), (4, 64), (5, 125) \} \] As each input \( x \) yields a unique output \( y \) (specifically, \( y = x^3 \)), \( R \) is a function.