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GO Classes DPP | TOC|REGULAR EXPRESSION

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Let $\mathrm{p}, \mathrm{q}$, and r be three regular expressions over the alphabet $\Sigma=\{a, b\}$.

  • $p=a(a+b)^* b$
     
  • $q=(a+b)^* a b(a+b)^*$
     
  • $r=a a^* b b^*$

Which of the following represents the correct relationship between the languages $L(p), L(q)$, and $L(r)$ generated by these regular expressions?

  1. $L(r) \subseteq L(p)$ and $L(p) \subseteq L(q)$
     
  2. $L(p) \subseteq L(r)$ and $L(r) \subseteq L(q)$
     
  3. $L(q) \subseteq L(p)$ and $L(p) \subseteq L(r)$
     
  4. $L(r) \subseteq L(q)$ and $L(q) \subseteq L(p)$

1 Answer

1 1 vote
Basic conclusion with string  like q can generate aba but p can't and p can generate abab but r can't  so p is subset of q and r is subset of p
OR

simply try to iterate the lang then u'll find ans A.
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