If r1 and r2 are regular expressions, then which of the following are correct.…

2026

If r1 and r2 are regular expressions, then which of the following are correct.

A. L(r1 + r2) = L(r1) ∪ L(r2)

B. L(r1 . r_2) = L(r1) L(r2)

C. L((r1)) = L(r1)

D. L(r1*) = (L(r1))*

Choose the correct answer from the options given below:

  1. A & B Only

  2. B, C & D Only

  3. A, C & D Only

  4. A, B, C & D

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

Attempted by 109 students.

Show answer & explanation

Correct answer: D

All four statements are fundamental properties of regular expressions. Statement A is correct because the union operator '+' combines languages from both expressions, resulting in their set union. Statement B is valid as concatenation '.' produces strings formed by appending any string from L(r2) to any string from L(r1). Statement C holds true since parentheses only affect precedence and do not change the language recognized. Statement D is accurate because the Kleene star '*' denotes zero or more repetitions of strings from L(r1). Since all individual statements (A, B, C, and D) are theoretically correct properties of regular expressions, the option containing all four is the right choice.

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