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How many states are there in the minimal DFA that accept the following language?

$L= \{x \mid x$ is a binary string with number of $0$'s divisible by $2$ and number of $1$'s divisible by $3 \}$

  1. $6$
  2. $5$
  3. $3$
  4. $2$
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While checking the divisibility of a number by 2, the possible cases are:- remainder 0 or 1 i.e. 2 cases. Similarly, for checking divisibility by 3, there are 3 possible cases, remainder 0,1 or 2. Therefore in total we have 2*3 = 6 possible states to be drawn in the minimal DFA.
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