Introduction to Logic

Exercise 2.7 - Digital Circuits

Consider the digital circuit described in section 2.7. Suppose we set nodes p, q, and r to be on, and we observe that all of the other nodes are on. Running our evaluation procedure, we would see that the first sentence in our description of the circuit is not true. Hence the circuit is malfunctioning. Is there any combination of inputs p, q, and r that would result in all other nodes being on in a correctly functioning circuit? If so, select one such combination. Otherwise, select the "impossible" option.

Hint: To answer this, you need consider a truth table with just eight rows (the possible values for nodes p, q, and r) since all other nodes are observed to be on.