So I have the P Channel MOSFET's Gate-Source voltage as 12-12 = 0V. This means the Drain and Source should be disconnected. However, I still see a 11.3V output from the drain. I have no idea what I am doing wrong. The threshold for the Vgs is -2V, and I am giving it 0V so it should be off. The DC power supplies are just 12V supplies.
My guess is that I should have a pull-down resistor from drain to the ground (around the LED and resistor) so that the drain pin is not floating when it is disconnected from the source. But, adding that resistor didn't solve the problem entirely.