Make DFA for divisible by 5 and exclude '0' string from that DFA So based on this minimal DFA will have 7 states and looks like below-
Approach is-
in divisible by 5 DFA there will be 5 equivalence classes{0,1,2,3,4} and as mentioned in question strings are start with 1 so we need to reject all string with 0.
is This Logic Right or Not?
we know modulo 5 DFA need minimum 5 state, in this all state work in cycle with each other state.
Here 0 is not start point means we have to reject it so 1 extra state for it and also State 0 is not doing its work so we need 1 Extra state for it to do the job of it.
so total 5+1+1=7
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