Cutoff leaves the collector output at the supply rail. 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 low input leaves the transistor in cutoff
The input equals the stated drop, so base current is 0 A and collector current is 0 A.
IB=0A,IC=0A
With no collector current, the output stays high
The collector resistor pulls the output to 12 V, so the checked output state is HIGH.