A pullup-idle-high scan treats the open switch as leaving no path to ground, so the pull-up resistor ties the output node to the source at V_out = 12 V. The arithmetic is exact only for the stated output voltages, source voltages, switch states, and rows in the ideal pull-up and ideal switch model. Real pull-up circuits add resistor tolerance, switch contact resistance, leakage, input impedance, supply tolerance, probe/calibration limits, finite precision, and measurement uncertainty.
A pull-up resistor gives an ideal high output when no switch path pulls the node down. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A pull-up ties the node to the source
With the switch open, the output node is connected to the source through the pull-up resistor.
open switch⇒no path to ground
The output is high
The checked output voltage is 12 volts. This ideal pull-up model ignores input leakage, capacitance, and real threshold ranges.