4. Design a circuit for the following situation. Three chemicals labeled A, B and C are stored in storage bins in a laboratory. It is dangerous to store all three chemicals together in one bin as well as to store each one separately. However storing two of the chemicals together in one bin is safe. Design a detection system such that the output Z=1 when a dangerous arrangement in a bin has been detected. The inputs to the system are the variables A, B and C. When a chemical is present the variable is true (e.g. A=1); if a chemical is not present the variable is not true (e.g. A=0).

a. Write Z as a sum of product terms as a function of A, B and C.

b. Write Z in little m notation.

c. Write Z as a product of sum terms as a function of A, B and C.

d. Write Z in big-M notation.