Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 2 / b / ii / Solution

A pair belongs to $R\circ R$ exactly when two successive $R$ steps connect its endpoints. The chain $a\to b\to c\to d$ has two such length-two paths, $a\to b\to c$ and $b\to c\to d$. HenceThis applies composition of relations directly; no other middle element gives a pair.