Answer
The open interval $(a, b)$ does not include $a$ and $b$ in the interval, while the closed interval $[a, b]$ includes both $a$ and $b$ in the interval.
An example of an interval that is neither open nor closed is:
$(2, 4]$
Work Step by Step
The open interval $(a, b)$ means the numbers $a$ and $b$ are not included in the interval/set. As a rule, a number beside a parenthesis is not included in the interval.
The closed interval $[a, b]$ means the numbers $a$ and $b$ are included in the interval/set. As a rule, a number beside a bracket is included in the interval.
An interval that is neither open nor closed is one that contains both a parenthesis and a bracket.
Thus, one example of an interval that is neither open nor closed is:
$(2, 4]$