regular expressions

Question

{(a* b)a } intersection {a*b*}, is this considered a regular language ? or not and how do i know ?

Comments

L(a*ba)= ba, aba, aaba, aaaba....<string end with ba >

L(a*b*)=€, a, aa,... b, bb,.... ab, aab, aaab, abb, abbb.... <any no of a's followed by any no of b's>

Intersection =common string

a*ba intersect a*b*= nothing =null language =regular

---

Regular Languages are closed under intersection .

this is always true

---

 Onika the regular expression $L=a^*ba$ is not end with ba.

---

then!?

---

$L=a^*ba$ produce strings like ${L=ba,aba,aaba,aaaba...\infty}$

but end with ba produce strings like ${L=ba,bba,bbba….,aba,aaba,abba,baba….\infty}$. it’s regular expression will be $(a+b)^*ba$

Here $a^*ba$ will not produce strings like $bba,abba,bbba,baba...$

Answer 1

Both are regular. So, yes.