A low-voltage lighting system is to use a binary logic control for a particular light. This light lies at the intersection point of a T-shaped hallway. There is a switch for this light at each of the three endpoints of the T. These switches have binary outputs 0 and 1 depending on their position and are named X1, X2, and X3. The light is controlled by a buffer driving a thyristor, an electronic part that can switch power-circuit current. When Z, the input to the buffer, is 1, the light is ON, and when Z is 0, the light is OFF. You are to find a function Z=F(X1,?X2,?X3) so that if any one of the switches is changed, the value of Z changes, turning the light ON or OFF.
Express the function using only NAND gates and invertors (NOT gates).