Consider the languages: L1=∅ L2={a}. Which of the following represents: L1 L2∗…
2021
Consider the languages:
L1=∅
L2={a}.
Which of the following represents:
L1 L2∗ U L1∗ ?
- A.
{∅}
- B.
{ε∅}
- C.
{π}
- D.
{ε}
- E.
Question not attempted
Attempted by 278 students.
Show answer & explanation
Correct answer: D
Step 1: L1 = ∅, the empty language. L2 = {a}.
Step 2: L2* is the Kleene closure of {a}, which is {ε, a, aa, aaa, ...}.
Step 3: L1L2* is the concatenation of ∅ with L2*, which results in ∅.
Step 4: L1* is the Kleene closure of ∅, which is {ε}.
Step 5: The union ∅ ∪ {ε} is {ε}.
Thus, the result is {ε}.
हिन्दी उत्तर:
चरण 1: L1 = ∅, खाली भाषा। L2 = {a}।
चरण 2: L2* {a} का क्लीनी क्लोजर है, जो {ε, a, aa, aaa, ...} है।
चरण 3: L1L2* ∅ का L2* के साथ संयोजन है, जो ∅ देता है।
चरण 4: L1* ∅ का क्लीनी क्लोजर है, जो {ε} है।
चरण 5: ∅ ∪ {ε} का संयोजन {ε} है।
इसलिए, परिणाम {ε} है।