Rework Example 9.2 to express and evaluate the logic formula to answer the question, “If the speed is below the set speed and the set speed is above the speed limit, then will the throttle be opened?”

Example 9.2

Consider the statement involving an automobile cruise control set at a certain speed (called the “set speed”): “Open the throttle if the speed is below the set speed and the set speed is not above the speed limit.” Express this as a logic formula, and evaluate the logic formula to answer the question: if the speed is below the set speed and the set speed is above the speed limit, then will the throttle be opened? Answer using these variables: the car’s speed is 50. Miles per hour, the set speed is 60. miles per hour, and the speed limit is 45 miles per hour.

Need: A binary logic formula expressing the statement, “Open the throttle if the speed is below the set speed and the set speed is not above the speed limit,” and an evaluation of the formula for the situation when the speed is 50. miles per hour, the set speed is 60. miles per hour, and the speed limit is 45 miles per hour.

Know: Any statement capable of being true or false can be represented by a variable having values 1 = true and 0 = false, and these variables can be connected by AND (∙), OR (+), and NOT (0).

How: Define variables corresponding to each of the statements, and use the three connectors to write a logic formula.