Question

What characterizes an Identity Relation?

Options

• Every element is related only to itself, i.e. \(I_A=\{(a,a):a\in A\}\).

• Every element of \(A\) is related to every element of \(A\).

• Every pair must have a reverse pair, but self-pairs are not required.

• No element of \(A\) is related to any element of \(A\).

Answer 1

In an Identity Relation, each element is related only to itself. Its ordered pairs have the form \((a,a)\), giving \(I_A=\{(a,a):a\in A\}\).