An equal-inputs-tie-rule scan forces both comparator inputs equal, here 6 V = 6 V, and applies the declared tie rule that selects the low rail so the output is never a caption guess. The arithmetic is exact only for the stated input voltages, output voltages, tie states, and rows in the ideal comparator model. Real comparators add input offset, hysteresis, noise, finite response time, reference tolerance, probe/calibration limits, finite precision, and measurement uncertainty.
The equality case is explicit so the comparator output is never a caption guess. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Equal inputs trigger the declared tie rule
Both comparator inputs are 6 volts.
6V=6V
This book ties equality to the low rail
The declared tie rule selects the low rail, so the output is 0 volts.