Question

Which one of the following regular expressions is NOT equivalent to the regular expression (a + b + c)${}^{\ast }$ ?

• A. $(a^{\ast }+b^{\ast }+c^{\ast }{)}^{\ast }$
• B. $(a^{\ast }{b}^{\ast }+c^{\ast }{)}^{\ast }$
• C. $(a^{\ast }{b}^{\ast }{c}^{\ast }{)}^{\ast }$
• D. $\left(\right(ab{)}^{\ast }+c^{\ast }{)}^{\ast }$

Answer 1

The correct option is D $\left(\right(ab{)}^{\ast }+c^{\ast }{)}^{\ast }$

In chance (a), (b) and (d). inside the parenthesis we can generate "a" , "b" and "c" seprately and hence all three are same as $(a+b+c{)}^{\ast }$ In choice (c) the strings "a" and "b" cannot be generated seperately since "ab" is always together

So, Choice (c) is not same as $(a+b+c{)}^{\ast }$