CanonicalNormalForm
Question 1 
Σm(4,6)  
Σm(4,8)  
Σm(6,8)  
Σm(4,6,8)

Question 1 Explanation:
f= f_{1}* f_{2} + f_{3}
f_{1}*f_{2} is intersection of minterms of f_{1} and f_{2}
f= (f_{1}*f_{2}) + f_{3} is union of minterms of (f_{1}*f_{2}) and f_{3}
Σm(1,6,8,15)= Σm(4,5,6,7,8) * f_{2} + Σm(1,6,15)
Options A, B and D have minterm m_{4} which result in Σm(1,4,6,15), Σm(1,4,6,8, 15) and Σm(1,4,6,8, 15)respectively and they are not equal to f.
Option C : If f_{2}= Σm(6,8)
RHS: Σm(4,5,6,7,8) * Σm(6,8) + Σm(1,6,15)
=Σm(6,8) + Σm(1,6,15)
= Σm(1,6,8,15)
= f= LHS
f_{1}*f_{2} is intersection of minterms of f_{1} and f_{2}
f= (f_{1}*f_{2}) + f_{3} is union of minterms of (f_{1}*f_{2}) and f_{3}
Σm(1,6,8,15)= Σm(4,5,6,7,8) * f_{2} + Σm(1,6,15)
Options A, B and D have minterm m_{4} which result in Σm(1,4,6,15), Σm(1,4,6,8, 15) and Σm(1,4,6,8, 15)respectively and they are not equal to f.
Option C : If f_{2}= Σm(6,8)
RHS: Σm(4,5,6,7,8) * Σm(6,8) + Σm(1,6,15)
=Σm(6,8) + Σm(1,6,15)
= Σm(1,6,8,15)
= f= LHS
There is 1 question to complete.