I know that if a language class is closed under operation X then the problem  is decidable.for eg: Intersection of two CSL is CSL? this problem is decidable because it is already proved that CSL follow intersection closure property.But what if language is not closed under the operation.for eg: problem: Is intersection of two CFL is CFL or not? as CFL/DCFL is not closed under intersection. then is this true saying that not following closure opertion implies Undecidable problem?My approach:This problem is same as saying that A given CSL is CFL or not? because intersection of two CFL's is CSL for sure. as every CSL is RE then can we also say this problem as A RE is CFL or not? if my last statement is true then by using rice theorem this problem must be undecidable and even not RE.how to approach these type of question when a language is not closed under the given operation?
Closure property and undecidability
undecidability