# decidability

184 views
intersection of two recursive lang is recursive

is this problem decidable or not?
0
this is closure property of recursive languages so its always true and hence decidable.
0
Recursive languages are closed under Intersection. So that statement is always True which makes it decidable.

This is a trivial fact as it follows from closure property that intersection of two recursive language is a recursive language for sure..Hence we can say that this property is decidable..

In fact

Any closure property if satisfied for a given class of language and given operation, then the problem that the resultant language after applying that particular operation is also in the same class is  decidable..

selected

## Related questions

1
243 views
$L=\left \{< M_{1},M_{2}> \text{such that L}(M_{1})\prec L(M_{2}) \right \}$ is it recursive enumerable? here $L\left ( M_{1} \right )\prec L\left ( M_{2} \right )$ signifies language $L\left ( M_{1} \right )$ is reducible to $L\left ( M_{2} \right )$
From http://www.cs.rice.edu/~nakhleh/COMP481/final_review_sp06_sol.pdf $L_{26}=\{<M>|$ M is a TM such that both L(M) and $\lnot L(M)$ are infinite $\}$ I was unable to get proof given in pdf above.Can anyone explain, if someone got it.