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Identify the class of L

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Consider

  • $L_1 = \left\{a^nb^nc^md^m \mid m,n \ge 1\right\}$
  • $L_2 = \left\{a^nb^n \mid n \ge1\right\}$
  • $L_3 = \left\{(a+b)^*\right\}$


Intersection of $L_1$ and $L_2$ is

(A) Regular (B) CFL but not regular (C) CSL but not CFL (D) None of these
 

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Regular.
 $L_1 \cap  L_2$
 $= \{abcd,aabbcd,aaabbbccdd,\dots\} \cap \{ab, aabb, aaabbb,\dots\}$
 $= \emptyset.$
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