Dark Mode

92 views

2 votes

Let $r_1$ and $r_2$ be two regular expressions. They symbol $\equiv$ stands for equivalence of two regular expressions in the sense that if $r_1 \equiv r_2$, then both regular expressions describe the same language. Which of the following is/are $\text{FALSE}$?

- $\left(r_1 r_2\right)^* r_1 \equiv r_1\left(r_2 r_1\right)^*$
- $\left(r_1^* r_2\right)^* r_1^* \equiv\left(r_1+r_2\right)^*$
- $\left(r_1^* r_2^*\right)^* \equiv\left(r_1+r_2\right)^*$

- Only (i) is false
- Only (ii) is false
- Only (iii) is false
- Both (i) and (iii) are false
- None of the above