UGC-NET | UGC NET CS 2016 Aug – III | Question 24

Consider the following identities for regular expressions:
(a) (r + s)* = (s + r)*
(b) (r*)* = r*
(c) (r* s*)* = (r + s)*
Which of the above identities are true?
(A) (a) and (b) only
(B) (b) and (c) only
(C) (c) and (a) only
(D) (a), (b) and (c)

Answer: (D)
Explanation:

• (r + s)* will generate any strings containing r or s or both. We can draw DFA for (r + s)* and it is same as (s + r)*. It is a regular expression.
• (r*)* will generate any string containing r and its DFA can be drawn easily and it is same as r*. It is also a regular expression.
• (r* s*)* will generate any strings containing r or s or both. We can draw DFA for (r* s*)* and it is same as (r + s)*. It is a regular expression. All option are true.

So, option (D) is correct.
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