Open-and shut-case is an idiom. We will examine the meaning of the common idiom open-and-shut case, where it came from, and some examples of its idiomatic usage in sentences.
An open-and-shut case is a situation or dispute that is easily decided; the correct decision is without a doubt. The expression open-and-shut case is often used to describe a legal matter where the facts are indisputable; however, the term open-and-shut case can be used to mean any unarguable dispute. The term open and shut came into use in the 1840s in the United States to mean straightforward; the term open-and-shut case became popular beginning in the 1920s. Note that open-and-shut is hyphenated in this phrase, because it is an adjective that appears before a noun.
Examples
A new report on social media and racism presents an open-and-shut case that the online platforms are fueling the spread of antisemitism and helping stoke the hatred that is tearing our society apart. (Las Vegas Sun)
“Never, Sir,” he responded when asked whether he thought the Oaks was an open-and-shut case. (Jamaica Gleaner)
We actually see the clays there, and they can explain the radar observations, so at this point it feels like an open-and-shut case, he says. (Forbes)