GATE CS 2014 Set 2 — Question 25
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Theory of Computation → Finite Automata & Regular Languages → Closure Properties (Regular)
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Question
If and , consider
(I) is a regular language
(II)
Which one of the following is CORRECT?
(I) is a regular language
(II)
Which one of the following is CORRECT?
Correct answer
(A) Only (I)
Solution
Given and .
The concatenation .
This corresponds to the regular expression , so is a regular language. Thus, (I) is TRUE.Statement (II) claims . This set represents strings with an equal number of 's and 's. However, the concatenation of and allows the number of 's and 's to be independent (e.g., but ). Thus, (II) is FALSE.
The concatenation .
This corresponds to the regular expression , so is a regular language. Thus, (I) is TRUE.Statement (II) claims . This set represents strings with an equal number of 's and 's. However, the concatenation of and allows the number of 's and 's to be independent (e.g., but ). Thus, (II) is FALSE.
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