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iam not getting when to use cross product or union of dfa to  join two dfa can someone tell me

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Yeah well! I can help you..

Suppose in a given string a's are divisible by 2 and/or b's divisible by 3 then to find product automata cross product of states of both automata should be done....

In both And opn and OR opn cross product should be done
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you go for union when you have two possible language generated by grammar Suppose you have to Generate a language over {a,b}  having different input in initial as well as final..here first language starting with either a,b and end with a,b...i hope u got it...

and you go for cross product whenever two different language generated by grammar adding with either OR,NOT,AND...

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