Question

Which statement defines a Universal Relation?

Options

• Every element of \(A\) is related to every element of \(A\), i.e. \(R=A\times A\).

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

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

• No element of \(A\) is related to any element of \(A\), i.e. \(R=\phi\).

Answer 1

A Universal Relation relates every element of \(A\) to every element of \(A\). Therefore, it contains all ordered pairs in \(A\times A\), so \(R=A\times A\).