3. (a) 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 end points of the T. these switches have binary outputs 0 and 1 depending on their position and are Names X1, X2, and X3. The light is controlled by an amplifier driving a thyristor. When Z, the input to the amplifier, is 1 the light is
ON and when Z is 0, the light is OFF. Find the 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.
(b) the function for Z is not unique. How many different functions for Z are there?