Consider the following two finite automata 𝐷1 and 𝐷2 Which of the following…
2026
Consider the following two finite automata 𝐷1 and 𝐷2
Which of the following statements is/are true?
- A.
𝐿(𝐷1 ) = 𝐿(𝐷2 )
- B.
L(𝐷1) is a proper subset of 𝐿(𝐷2 )
- C.
𝐿(𝐷1 ) ∩ 𝐿(𝐷2 ) = { 𝜖}
- D.
(𝐿(𝐷1 ) ∪ 𝐿(𝐷2))∗ consists of all strings in {0,1}∗ whose length is divisible by 3
Attempted by 21 students.
Show answer & explanation
Correct answer: C, D
Option A is false (languages differ).
Example - 000 is accepted by D1 but not by D2
Option B is false (D1 has strings not in D2).
Example - 000 is in D1 but not in D2
Option C is Correct1
The intersection is just {ε}.
Option D is true e.g., '100' has length 3 but is not in either language).