Show that the $\vee: R \times R \rightarrow R$ given by $(a, b) \rightarrow \max\{a, b\}$ and the $\wedge: R \times R \rightarrow R$ given by $(a, b) \rightarrow \min\{a, b\}$ are binary operations.

(N/A) binary operation $\ast$ on a set $S$ is a function $\ast: S \times S \rightarrow S$.
For the operation $\vee: R \times R \rightarrow R$ defined by $(a, b) \rightarrow \max\{a, b\}$,for any pair $(a, b) \in R \times R$,the value $\max\{a, b\}$ is a unique real number that belongs to $R$.
Since every pair $(a, b)$ maps to a unique element in $R$,$\vee$ is a binary operation.
Similarly,for the operation $\wedge: R \times R \rightarrow R$ defined by $(a, b) \rightarrow \min\{a, b\}$,for any pair $(a, b) \in R \times R$,the value $\min\{a, b\}$ is a unique real number that belongs to $R$.
Since every pair $(a, b)$ maps to a unique element in $R$,$\wedge$ is also a binary operation.