If $A=\{1,2,3,4,5\}$ and let $\ast$ is an operation on $A$ such that $a\ast b=\min \{a,b\}$. Which of the following is true?

For $\ast$ to be a binary operation on set $A$, it must satisfy the closure property: for all $a,b\in A$, $a\ast b$ must also be in $A$.Since $a$ and $b$ are elements of $A=\{1,2,3,4,5\}$, the minimum of any two elements in $\{1,2,3,4,5\}$ will always be an element of the same set $\{1,2,3,4,5\}$.Therefore, $\ast$ satisfies closure and is a binary operation on $A$.