Question

A relation \(R\) on \(A\) is reflexive when which condition holds?

Options

• \((a,b)\in R\Rightarrow(b,a)\in R\) for every \(a,b\in A\).

• \((a,b)\in R\) and \((b,c)\in R\Rightarrow(a,c)\in R\).

• \(R=A\times A\).

• \((a,a)\in R\) for every \(a\in A\).

Answer 1

Reflexivity requires every element to be related to itself. Therefore, the self-pair \((a,a)\) must belong to \(R\) for every \(a\in A\).