In a certain application, four inputs A, B, C, D (both true and complement forms available) are fed to logic circuit, producing an output F, which operates a relay. The relay turns on when  for the following states of the input  and . States ‘1000’ and ‘1001’ do not occur, and for the remaining states, the relay is off. Minimize F with the help of a Karnaugh map and Find the minimum number of 3 – input NAND gates required to realize this.