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## Q.52) Consider the following languages over the alphabet ∑= {a,b,c}. Let L1 = {an bncm | m, n >= 0 } and L2 = {ambncn| m, n >= 0}. -gate computer science 2017

**Which of the following are context-free languages ?**

**I. L1 ∪ L2**

**II. L1 ∩ L2**

**A)**

**I only**

**B)**

**II only**

**C)**

**I and II**

**D)**

**Neither I nor II**

By:satyashiromani

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## Answers

**A) I only**

Explanation:

Union of context free language is also context free language.

L1 = { an bn cm| m >= 0 and n >= 0 } and

L2 = { am bncn| n >= 0 and m >= 0 }

L3 = L1 ∪ L2 = { anbncm∪ ambncn| n >= 0, m >= 0 } is also context free.

L1 says number of a’s should be equal to number of b’s and L2 says number of b’s should be equal to number of c’s. Their union says either of two conditions to be true. So it is also context free language.

Intersection of CFG may or may not be CFG.

L3 = L1 ∩ L2 = { anbncn| n >= 0 } need not be context free.

This explanation is contributed by

__Deepak Raj__deepuckraj

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