Question

A set of pedestrian lights is quite near to a set of traffic lights at a road junction. When the pedestrian lights are red, they are controlled by the gradment of code given below. The code fragment contains Boolean variables b,r and t corresponding to the following propositions. b: The button has been pressed. r : The pedestrian lights have been red for three minutes. t : There is too long a queue at the traffic lights. var lights in mstring if (b/\r) then \{ lights.setString ("Change to green") \} //(1) if (b /\t ) then \{ lights.setString ("No change") \} //(2) if (NOT (b)) then \{ lights.setString ("No change") \} //(3) if ( t ) then \{ lights.setString ("No change") \} //(4) if (b/\NOT(r)) then \{ lights.setString ("No change") \} //(5) (a) Complete an outcome table for this fragment, with the Boolean variables in the order b,r, t. (In your table, the two possible outcomes can be abbreviated as "Change" and "No change".) In each case, indicate which code statement (labelled (1) - (5) above) actually determines the outcome. Using your outcome table and the interpretations of the atomic propositions given above, describe in English the circumstances under which this code will have the outcome "Change to green". (b) Use your outcome table to draw up a nested conditional statement to replace the original code.

Answer 1

The pedestrian lights will change to green only when the button has been pressed and they have been red for three minutes provided there isn't a long queue at the traffic lights.

Step-by-step explanation:

The question relates to the programming logic for a set of pedestrian lights near traffic lights, using Boolean variables to represent different conditions. To determine when the pedestrian lights change to green, we construct an outcome table based on the given code fragment:

• 
  
• b: The button has been pressed.
• 
  
• r: The pedestrian lights have been red for three minutes.
• 
  
• t: There is too long a queue at the traffic lights.

An outcome table would be created to cover all combinations of these Boolean variables, and from there, we can see that the pedestrian light will change to green only when both b (the button has been pressed) and r (the lights have been red for three minutes) are true. Any other combination would result in 'No change' as specified by the different conditions in the existing code.

To simplify the existing code using a nested conditional statement, we would write:

if (b) {
if (r && !t) {
lights.setString("Change to green");
} else {
lights.setString("No change");
}
} else if (t) {
lights.setString("No change");
}

This nested conditional statement evaluates the conditions in a logical order, starting with whether the button has been pressed, then checking the duration the light has been red and the length of the traffic queue before determining the appropriate action for the pedestrian lights.