CONSIDER LANGUAGE L=(a+b)^*
substrings property is not closed under regular languages.
suppose substrings for the above language L={ab,aabb,aaabbb,....}
it is {$a^{n}b^{n}$/n>=0}
it is not regular language.otherwise substrings are L={a,aba,..} it is regular.so may or may not regular.
so substring property is not closed under regular languages.
2)infinite intersection
Let the language $L_{i}={a^{*}-{a^{x_{i}}}$
Now consider L=L= The infinite intersection of the sequence of languages L1,L2,…L1,L2,…. That is,
L=$\bigcap_{i=1}^{\aa }L_{i}=L_{1}\cap L_{2}\cap ..........$
so L={a$^{p}$| p is prime}.
if L={ab}^{aabb}^{a}^{b}......
it's intersection is L={$\Phi$},it is regular.so may or may not regular.
so infinite intersection is not closed under this property.