A controlled switch can make a high input produce a low output in this ideal pull-up model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Open input gives high output
When the controlled switch is open, the output is 12 volts. The controlled switch is only the circuit role of a transistor here; gain, saturation, base or gate current, and CMOS details are deferred.
open input⇒Vout=12V
Closed input gives low output
When the controlled switch closes, the output becomes 0 volts.