How to design an AND gate for 24V AC Thermostat Connection
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A suggested scheme.


Furnace Low will turn on if either input is on.
Furnace High will turn on if both inputs are on.


A pair of 24 V AC coil, single-pole relays - one with changeover contact - should be all that is required.




  Just to close the loop then, there isn't really a thing as AC logic gate ICs the way there are DC logic gates, or similar shortcuts like how two diodes can make an OR gate with DC?


There isn't an easy way to do it in the same way as there is with DC logic. I'm sure there were some sort of electro-magnetic devices used in times past to achieve some sort of AC logic without using moving contacts. 









simulate this circuit

Figure 2. An SSR implementation of the scheme. D1 to D4 represent the input side of the SSR which will be more complex than a simple LED.

This arrangement may not switch reliably due to the AC control of the opto drivers running on low voltage. The LEDs may turn on the opto-triacs rather late in each half-cycle.