Question

Let \(A\) be the set of real numbers and define \(aRb\) when \(a-b<5\). Which calculation demonstrates that \(R\) is reflexive?

Options

• \(4-(-4)=8\nless 5\)

• \(a-a=0<5\)

• \(2-8=-6<5\)

• \(8-2=6\nless 5\)

Answer 1

For every real number \(a\), \(a-a=0\), and \(0<5\). Therefore, \(aRa\) holds for every \(a\in A\), so the relation is reflexive.