a. [4 marks] Prove that the dual of the exclusive-OR is also its complement. b. [3 marks] Simplify ABC+AC+ABCE+ACD using basic identities of Boolean algebra. c. [3 marks] By using truth table method, prove that (A+B)=AB is true, where A and B are two binary variables. d. [2 marks] Write the duality form of the equation ABC+BCD+BC+CD=B+CD. e. [3 marks] Using the K-Map, simplify the following expression AB+AC+BC+ABCC. Note that you need to provide the K-Map and draw the circuit