The maximum number of transition which can be performed over a state in a DFA where alphabet set is {a,b,c}a.3b.4c.2d.1

The maximum number of transitions that can be performed over a state in a DFA (Deterministic Finite Automaton) where the alphabet set is {a,b,c} is 3.

Here's why:

1. A DFA is a theoretical model of computation from automata theory. It is a finite state machine that accepts or rejects strings of symbols and only produces a unique computation (or run) of the automaton for each input string.

2. The number of transitions from a state is equal to the number of unique input symbols (or alphabet set) that the DFA can process. In this case, the alphabet set is {a,b,c}.

3. Therefore, from each state, there can be exactly one transition on 'a', exactly one transition on 'b', and exactly one transition on 'c'.

So, the maximum number of transitions which can be performed over a state in a DFA where alphabet set is {a,b,c} is 3. Hence, the answer is (a) 3.