Q.Let $A = \{1, 2, 3, 4, 5\}$. A relation $R$ on $A$ is defined by $R = \{(a, b) : b = a + 1\}$. Write $R$ in roster form and state its domain and range.

Apply $b = a + 1$ to each $a \in A$, keeping only pairs whose second value is also in $A$; then read off first and second components.

Apply the rule $b = a + 1$ for each $a \in A = \{1,2,3,4,5\}$, keeping the pair only when $b$ is also an element of $A$ (since $R$ is a relation on $A$):

• $a = 1 \Rightarrow b = 2 \in A$: $(1, 2)$
• $a = 2 \Rightarrow b = 3 \in A$: $(2, 3)$
• $a = 3 \Rightarrow b = 4 \in A$: $(3, 4)$
• $a = 4 \Rightarrow b = 5 \in A$: $(4, 5)$
• $a = 5 \Rightarrow b = 6 \notin A$: no pair

So

$R = \{(1, 2),\ (2, 3),\ (3, 4),\ (4, 5)\}.$ …

The key omission is forgetting to drop $a = 5$ (whose image $6$ is not in $A$); including $(5, 6)$ would wrongly e …