Answer

Correct Option: (i) 3 states and 6 transitions (for residue mod 3 Moore machine)

Explanation

To produce residue mod 3, need 3 states corresponding to remainders $0,1,2$.

• Alphabet: e.g., binary or unary? For general input, Moore machine that outputs residue after each symbol needs 3 states.
• Transitions: For binary alphabet $\{0,1\}$, from each of 3 states there are 2 outgoing transitions ($0$ and $1$): $3 \times 2 =6$ transitions. Formula: new remainder $r' = (r \times base + digit) \bmod 3$.

If alphabet were $\{0\}$ unary, transitions =3; but typical exam assumes binary/decimal digit input, hence 6.

Other options (3,5), (2,4) insufficient to represent 3 residues.

Final Answer

3 states, 6 transitions → Option (i). If input alphabet size $|\Sigma|=k$, transitions $=3k$.