Question

$\text{Which of the following regular expressions}\text{describes the language over}\{0,1\}$
$\text{consisting of string that contain exactly two 1's ?}$

Answer 1

$(0+1{)}^{\ast }11(0+1{)}^{\ast }$ $\text{represents all string which has 11 as}$ $\text{substring.}$

$0^{\ast }{110}^{\ast }$ $\text{represents all string with exactly two}$ $\text{consecutive 1's.}$

$0^{\ast }{10}^{\ast }{10}^{\ast }$ $\text{represents all string with exactly two}$ $\text{1's but need not be consecutive.}$

$(0+1{)}^{\ast }1(0+1{)}^{\ast }1(0+1{)}^{\ast }$ $\text{represents all string with atleast two}$ $\text{1's.}$