Which of the following are correct on regular expressions?
a. $\varphi + L = L + \varphi = L$
b. $\epsilon L = L\epsilon = L$
c. $\varphi L = L\varphi = \varphi$
d. $\varphi L = L\varphi = L$
Choose the correct answer from the options given below:
🎥 Video solution / Text Solution of this question is given below:
Statement a:
Union with empty language gives the same language.
$\varphi + L = L$
So, statement a is true.
Statement b:
Concatenation with empty string does not change the language.
$\epsilon L = L\epsilon = L$
So, statement b is true.
Statement c:
Concatenation with empty language gives empty language.
$\varphi L = L\varphi = \varphi$
So, statement c is true.
Statement d:
This says concatenation with empty language gives $L$, which is false.
So, statement d is false.
Correct statements are:
a, b and c only