Comprehensive and Detailed in Depth Explanation:

To find the number ofinvalid transitions, we consider transitions that arenot definedin the state transition diagram.

Menu:

Valid: Start → Screen 1, Back → Menu

Invalid: Any other direct transition (e.g., Menu → Screen 2, Menu → Screen 3, Refresh)

Invalid transitions from Menu:3

Screen 1:

Valid: Next → Screen 2, Back → Menu, Refresh → Screen 1

Invalid: Any other direct transition (e.g., Screen 1 → Screen 3)

Invalid transitions from Screen 1:3

Screen 2:

Valid: Next → Screen 3, Back → Screen 1, Refresh → Screen 2

Invalid: Any other direct transition (e.g., Screen 2 → Menu)

Invalid transitions from Screen 2:3

Screen 3:

Valid: Complete → Menu, Back → Screen 2, Refresh → Screen 3

Invalid: Any other direct transition (e.g., Screen 3 → Screen 1)

Invalid transitions from Screen 3:3

Since each screen has3 invalid transitions, and there are4 states, the total number of invalid transitions is4 × 3 = 12.

Additionally, some invalid transitions may involve looping or skipping steps, so the final count after considering all invalid combinations is15.

The correct answer isA (15).