Automating Filling of Humidifier - Logical OR Gate
What you want is more than a gate. A gate is combinatorial, meaning that its output is simply a function of its inputs. It has no memory. Whenever you have the same inputs, you'll always have the same output.

But your requirement is different. When the tank is half empty, and one switch is on, and one is off, should the tank be filling or not? Answer, it depends. This cannot be achieved with a simple gate.

What you need is a Set Reset Latch (SR-Latch). This latch is made from two gates wired together.



A high pulse on the S (set) input flips the output into one state. The state stays until a high pulse on the R (reset) input flips it the other way.

So, how does this work in practice? Imagine the tank is half full, and the switches are wired so that their output is low when the tank is half full. The latch is currently in the 'not filling' state.

When the water level reaches the bottom switch, it causes the output to go high, flipping the latch into the 'filling' state. The filling continues, even as the water level goes back above the bottom switch, and continues until the water level reaches the top switch. This causes the top switch to flip the latch back into the 'not filling' state.



Now, you wouldn't bother to make this latch out of individual transistors. It would be simpler to buy a chip containing NOR gates, like the 4001 Quad NOR chip. These cost less than 50p.



Alternatively, make it even easier. Buy a chip with an SR latch already on it, like the 74LS279:



This chip actually contains NAND based latches, rather than NOR based ones. The concept is the same, but the inputs are active low, rather than active high.



Added:

So how do you use the latch to switch a 120v AC valve? You certainly don't need to make a latch from 120v transistors! You can use a low voltage to switch any kind of high voltage or current, you just need the right kind of interface components.

You should use a relay to switch the high voltage, and a transistor to interface between the latch and the relay. See the answer to another question: How can i drive a 5v 120VAC 80mA with 15A contacts with a raspberry pi? for details about how to do that. There you will see a diagram. On the diagram, where is says 'GPIO', that's the signal from the output of your latch. Where it says L_COIL, that's the coil of your relay. You'll need a relay which can be energised with, say, 5v. But the contacts need to be rated for 120v AC.