Which of the following is NOT a valid identity in regular expression algebra?
2025
Which of the following is NOT a valid identity in regular expression algebra?
Answer: B. R* = ∅ — In regular expression algebra: Rε=R is valid because concatenating with epsilon (empty string) does not change the expression. R+ = RR∗ is valid because one…
- A.
Rε = R
- B.
R* = ∅
- C.
R+ = RR*
- D.
R + ∅ = R
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Correct answer: B
In regular expression algebra:
Rε=R is valid because concatenating with epsilon (empty string) does not change the expression.
R+ = RR∗ is valid because one or more repetitions can be expressed as one occurrence followed by zero or more occurrences.
R+∅=R is valid because union with the empty set does not change the language.
However, R∗ =∅ is NOT valid.
The Kleene star R∗ always contains at least the empty string ε, so it can never be equal to the empty set.
Therefore, Option B is correct.