Question

Using DeMorgan's Law, write an expression for the complement of F if F(w,x,y,z) = xyz'(y'z + x)'+ (w'yz+x').

Answer 1

The complement of the function F(w,x,y,z) is obtained by applying DeMorgan's laws to each conjunction and disjunction within the function, distributing the complements inside parentheses and simplifying the expression accordingly.

Step-by-step explanation:

The student has asked to write the complement of the function F(w,x,y,z) using DeMorgan's Laws, when given F(w,x,y,z) = xyz'(y'z + x)'+ (w'yz+x'). To find the complement of F, denoted as F'(w,x,y,z), we must apply DeMorgan's Laws which state that the complement of a conjunction (AND) is the disjunction (OR) of the complements and vice versa.

Step-by-step explanation:

1. First, we take the complement of the entire function F.
2. Then, according to DeMorgan's law, we distribute the complement inside the brackets: (XYZ')' becomes X'+Y+Z and (Y'Z+X)' becomes (Y'+Z)'+X'.
3. Next, observe that (Y'Z)' transforms into Y+Z' and (Y'+Z)'+ by DeMorgan's laws becomes YZ.
4. Finally, combine all the terms with OR between them and simplify where possible.

Thus, applying these rules, the complement of F, F'(w,x,y,z), would be:

F'(w,x,y,z) = (X'+Y+Z)(Y+Z')(X'+WYZ')