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We described the $"$product construction$"$ that took two DFA's and constructed one DFA whose language is intersection of the languages of the first two.

- Show how to perform the product construction on NFA's (without $\in$ transitions).
- Show how to perform the product construction on $\in-$NFA's
- Show how to modify the product construction so the resulting DFA accepts the difference of the languages of the two given DFA's.
- Show how to modify the product construction so the resulting DFA accepts the union of the languages of the two given DFA's.