Test by Bikram | Mock GATE | Test 4 | Question: 44

Question

Which of the following regular expressions describes the same set of strings as  $\left ( a^*+b \right )^*$  $\left ( c+d \right )$?

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

Answer 1

we know this identity:

$(a+b)$*$=(a$*$ + $b$*)* = (a$*$b$*$)$*$ = (a$*$ + b )$*$ = (a +b$*$)$*$ = a$*$(ba$*$)$*$ = b$*$(ab$*$)$*

$( a$*$ + b )$*$  (c + d) = (a+b)$*$(c + d)$

                            $=$ $(a+b)$*$c + (a+b)$*$d$

option $C$...