Question

Why is \(R=\{(1,4),(2,3),(3,2),(4,1)\}\) not a function on \(A=\{1,2,3,4,5\}\)?

पर्याय

• The output \(4\) belongs to \(A\).

• Inputs \(1\) and \(4\) have different outputs.

• Input \(5\) has no output.

• Input \(1\) has exactly one output.

Answer 1

A function on set \(A\) must use every element of \(A\) as an input. Here, input \(5\) is left without an output, so the relation fails the definition of a function on \(A\).