Question

Let Σ = { a, b } , and consider the language L = { a n : n is even } ∪ { b n : n is odd } . Draw a graph representing a DFA (not NFA) that accepts this language.

Answer 1

you can see that every string in this language either contains all a's in even no or all b's in odd number but there is no string such that it contains both a and b in any number .

you can see in above graph when i am trying to accept a string with all a's in even number if in state q1 or q2 i see any b i move to q5 which is dead so that if string enters this state a string can never come out of this state and it is rejected

DFA Graph a q a 226 6 95 90 1) а ta 6 24 qo is street state 90, 92, 93 are accepting states or final states q5 is dead state

Similarly when i am trying to accept a string with all b's if i see any a in q3 and q4 states i move to q5 or dead state

If you are having any doubts please ask i will answer asap