Question

Which two of the following four regular expressions are equivalent?

(i) $\left(00{)}^{\ast }\right(ϵ+0)$

(ii) $(00{)}^{\ast }$

(iii) $0^{\ast }$

(iv) $0(00{)}^{\ast }$

• A. (i) and (ii)
• B. (iii) and (iv)
• C. (i) and (iii)
• D. (ii) and (iii)

Answer 1

The correct option is C (i) and (iii)

(i) $\left(00{)}^{\ast }\right(ϵ+0)$

= $(00{)}^{\ast }ϵ+(00{)}^{\ast }0=0^{\ast }$

$\text{Even no. of 0' s and Odd no. of 0's}$
$\text{i.e., any number of 0's}$

(ii) $(00{)}^{\ast }=Evenno.of{0}^{\prime }s$

(iii) $0^{\ast }=anyno.of{0}^{\prime }s$

(iv) $0(00{)}^{\ast }=Oddno.of{0}^{\prime }s$

$\text{So (i) and (iii) are same.}$