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These are the two initial DFAs, and I need to construct a DFA that recognizes the intersection of the two languages accepted by the given DFAs, using closure properties.

Here is the first DFA:

DFA1

And here is the second DFA:

DFA2

My question is: if in the first automaton there is a transition on symbol b from state q0 to a sink state q3, then in the intersection automaton, is the state pair (q3, q1) also a sink state? Is that correct? The intersection automaton I found is made up of 6 states.

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