2.2 Relations

Identify Pairs: We substitute $x \in A$ and check if $y \in A$.

• $x=1 \implies y=2$. $(1, 2) \in R$.
• $x=2 \implies y=3$. $(2, 3) \in R$.
• $x=3 \implies y=4$. $(3, 4) \in R$.
• $x=4 \implies y=5$. $(4, 5) \in R$.
• $x=5 \implies y=6$. $(5, 6) \in R$.
• $x=6 \implies y=7$. But $7 \notin A$, so stop.

Roster Form: $R = \{ (1, 2), (2, 3), (3, 4), (4, 5), (5, 6) \}$.

Domain: First elements $\{1, 2, 3, 4, 5\}$.

Range: Second elements $\{2, 3, 4, 5, 6\}$.

Codomain: Set $A = \{1, 2, 3, 4, 5, 6\}$.