How are you going to get your input states into it?
Your circuit has two inputs. They need to be driven with logic levels - either high (1) or low (0).
That's what the switches are for. If you have some other source of logic levels, you don't need switches. But to make that circuit usable, you have to define what the inputs are driven from. Just calling them "V1" and "V2" doesn't give you enough information about what is driving those inputs. That's why I drew the battery and the switches.
If you have some other source to supply the V1 and V2 inputs, show us what it is. If it's the outputs from two logic ICs, then the circuit will work, as long as the "OUT1" and "OUT2" connection points are connected to a fully floating device such as an LED (with current limiting resistor).
In other words, if you don't want the battery and switches, what will you replace them with? Draw a circuit with that, and we can tell you if it will work. Or you can simulate it yourself.