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 \( R \) contains pairs where the second roll number is the cube of the first roll number. For example, if the roll numbers are \( 1, 2, 3, 4, 5 \), the elements of \( R \) will be: \[ R = \{ (1, 1), (2, 8), (3, 27), (4, 64), (5, 125) \} \] Since for each input \( x \), there is exactly one output \( y \) (i.e., \( y = x^3 \)), this relation satisfies the definition of a function. Thus, \( R \) is a function.