Question

In a standard Turing Machine \( T \), the transition function \( \delta (q, a) \) for \( q \in Q \) and \( a \in \Gamma \) is defined:

• A. For some, not necessarily all elements of \( (q, a) \in Q \times \Gamma \)
• B. For no element of \( (q, a) \in Q \times \Gamma \)
• C. For all elements of \( (q, a) \in Q \times \Gamma \)
• D. For a set of triples with more than one element

Hint:

In a Turing Machine, the transition function must be defined for all combinations of states and tape symbols to ensure proper operation.

Answer 1

The Correct Option is C

Step 1: Understanding the transition function.
In a Turing Machine, the transition function \( \delta \) specifies the next state based on the current state \( q \) and the symbol \( a \) read from the tape. The function is defined for all pairs \( (q, a) \), meaning for each state and tape symbol combination, there is a defined transition.

Step 2: Conclusion.
Thus, the transition function \( \delta \) is defined for all elements of \( (q, a) \in Q \times \Gamma \), making the correct answer (3).