Design a switching circuit with three inputs $($A$,$B$,$C$)$ and one output F$($A$,$B$,$C$).$ The$$ output function F$($A$,$B$,$C$)$ turns on $(1)$ when the binary number $($ABC$)$ represents a prime number $\{2,3,5,7\}$ and it turns off$(0)$ when the binary number $($ABC$)$ represents a not prime number $\{0,1,4\}.$

a$)$ Write the minimum SOP form to represent F

b$)$ Draw the logic circuit $($AND $-$ OR$)$

c$)$ Re$-$draw the circuit using only NAND gates only after you derive its corresponding expression