# Definition:Combinable

## Definition

### Relations

Let:

$(1): \quad \mathcal R_1 \subseteq S_1 \times T_1$ be a relation on $S_1 \times T_1$
$(2): \quad \mathcal R_2 \subseteq S_2 \times T_2$ be a relation on $S_2 \times T_2$

If $\mathcal R_1$ and $\mathcal R_2$ agree on $S_1 \cap S_2$, they are said to be combinable.

### Mappings

The concept is usually seen in the context of mappings:

Let:

$(1): \quad f_1: S_1 \to T_1$ be a mapping from $S_1$ to $T_1$
$(2): \quad f_2: S_2 \to T_2$ be a mapping from $S_2$ to $T_2$

If $f_1$ and $f_2$ agree on $S_1 \cap S_2$, they are said to be combinable.