TIFR CSE 2022 | Part B | Question: 8

Question

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 $\text{FALSE}$?

1. $\left(r_1 r_2\right)^* r_1 \equiv r_1\left(r_2 r_1\right)^*$
2. $\left(r_1^* r_2\right)^* r_1^* \equiv\left(r_1+r_2\right)^*$
3. $\left(r_1^* r_2^*\right)^* \equiv\left(r_1+r_2\right)^*$

 

• A. Only (i) is false
• B. Only (ii) is false
• C. Only (iii) is false
• D. Both (i) and (iii) are false
• E. None of the above