UGC NET CSE | June 2014 | Part 2 | Question: 09

Question

The context free grammar for the language $L= \left\{a^{n}b^{m}c^{k} \mid k = \mid n - m\mid , n \geq 0, m \geq 0, k \geq 0\right\}$ is 

• A. $S \rightarrow S_{1}S_{3}, S_{1} \rightarrow aS_{1}c \mid S_{2} \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$
• B. $S \rightarrow S_{1}S_{3}, S_{1} \rightarrow aS_{1}S_{2}c \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$
• C. $S \rightarrow S_{1} \mid S_{2}, S_{1} \rightarrow aS_{1}S_{2}c \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$
• D. $S \rightarrow S_{1} \mid S_{3}, S_{1} \rightarrow aS_{1}c \mid S_{2} \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$

Answer 1

AND WITH OPTION D WITH S1-->S3-->aS3b-->aS4b-->abS4cb-->abcb.....this is also not generated by the language SO ALL ARE FALSE

Comments

In D) S3 is giving abcb , which is not in string

So I think all option are false

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THANKS...NOW CHECK