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 $F$ $(\mathrm{ABCD})=1$ for the following states of the inputs $\text{(ABCD)}: '0000', '0010', '0101', '0110', '1101'$ and $'1110'$. States ' $1000^{\prime}$ and $'1001'$ do not occur, and for the remaining states, the relay is off. Minimize $F$ with the help of a Karnaugh map and realize it using a minimum number of $3$ - input $\text{NAND}$ gates.
