Question

Consider 2 scenarios:
C1: For DFA (ϕ, Ʃ, δ, qo, F),
if F = ϕ, then L = Ʃ*
C2: For NFA (ϕ, Ʃ, δ, qo, F),
if F = ϕ, then L = Ʃ*
Where F = Final states set
ϕ = Total states set
(a) Both are true (b) Both are False
(c) C1 is true, C2 is false (d) C1 is false, C2 is true

Answer 1

C1 is true.

C2 is not True but that doesn't mean it always false. C2 sometimes true some time false.

"C2: For NFA (ϕ, Ʃ, δ, qo, F), if F = ϕ, then L = Ʃ* . Where F = Final states set, ϕ = Total states set" is neither always TRUE nor always FALSE.

but even one case contradict then it considered as false. so answer is Option C.

Comments

Sir for DFA also If I dont make any transition then also , I will have the same criteria as accepting only ϵ

ϵ∈, so then why is C2 false , I am not getting the logic clearly ,plz clarify it again .

---

In DFA we have transitions for all symbols and all states are final states, so all strings will be accepted.

In NFA, there may be some symbols for which there is no transition. then all strings will not be accepted.

---

Very appropriate. If transition is not defined then it becomes undefined and hence, false in that case.

Answer 2

C1 is true and C2 is false.

Comments

In case of a NFA even if F = ϕ, there may be some states where we have no transitions defined for a particular symbol i.e Dead state rejections in NFA. Due to which, L ≠ Ʃ*.however this is not the case for dfa here

Answer 3

C1 is true, C2 is false

As in case of NFA even is F = ϕ, dead state rejection is there so L ≠ Ʃ* .