Language accepted by NFA

Question

Consider the NFA below:

The above NFA acceptes all those binary strings which represents the decimal numbers and are
a. divisible by 6 only
b. dividible by 2 and 3 only
c. divisible by 2 or 3
d. None of these

Comments

is it answer c??

Answer 1

Ans. C.

• For option A: It will accept numbers divisivle by 6, but not 6 only. (will accept 4, 8, ...)
• For option B: It will accept number divisible by 2 and 3, but not 2 and 3 only ( will accept 9, which is divisible by 3 but not but 2)
• Otion C: it accept numbers which are either divisble by 2 or 3 (All numbers divisibile by this NFA is divisible by either 2 or 3 or both.)

Comments

but it does not accept string 10. 10 will end up the NFA in state $q_5$. Then how can we say that it "accepts **all** those binary strings which represents the decimal numbers and are divisible by 2 or 3"

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Instead of 10, if 2 is represented as 010 it will accept. Otherwise it will not accept (that means None of these will be the answer).