Mathematics

The key to analyzing this relation is to check each property by examining what pairs are actually in $R$ and what pairs would need to be there. Reflexivity asks whether every element relates to itself; symmetry asks whether whenever $a$ relates to $b$, then $b$ relates to $a$; and transitivity asks whether chains of relations close up (if $a \to b$ and $b \to c$, then $a \to c$). For part (iv), you'll need to identify which single pair is "missing" to make the relation satisfy all three properties simultaneously—think about which elements are currently isolated from the others.

The key to analyzing this relation is to check each property by examining what pairs are actually in $R$ and what pairs would need to be there. Reflexivity asks whether every element relates to itself; symmetry asks whether whenever $a$ relates to $b$, then $b$ relates to $a$; and transitivity asks whether chains of relations close up (if $a \to b$ and $b \to c$, then $a \to c$). For part (iv), you'll need to identify which single pair is "missing" to make the relation satisfy all three properties simultaneously—think about which elements are currently isolated from the others.