Dual output/dual input canceling 12v trigger
Take a look at your O2 signal. It is identical to i2, so there is no need to do anything with it.

The O1 signal can be realized using a simple inverter and an AND gate. 







simulate this circuit &ndash; Schematic created using CircuitLab

If you want to build something like this, you'll probably not want to buy two chips for such a simple job. You can implement the same using NAND gates. A NAND gate with it's inputs connected works as an inverter. We use one of them to replace the inverter, and another to turn the NAND gate back into an AND gate:







simulate this circuit

If you want to build the circuit you'll find chips with four NAND gates in it as TL7400 (a classic, works with 5V, so you need voltage translation) or the CD4011 which will work fine from a 12V supply.