Question

What should be checked to determine whether a relation is transitive?

Options

• Whether every element is related only to itself

• Whether every \((a,b)\) has the reverse pair \((b,a)\)

• Whether \((a,b)\) and \((b,c)\) together give \((a,c)\)

• Whether \(R=\phi\)

Answer 1

Transitivity is checked by following two related pairs in sequence. The presence of \((a,b)\) and \((b,c)\) requires the pair \((a,c)\) to be present.