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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.