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 F(w,x,y,z) is found by negating the function and applying DeMorgan's Law, resulting in the expression (x'+y+z)(y+z'+x')(w+y'+z')x.

Step-by-step explanation:

The student's question focuses on applying DeMorgan's Law to find the complement of a given logical function F(w,x,y,z). DeMorgan's Laws are rules in Boolean algebra that relate the logical operations of conjunction (AND) and disjunction (OR) in an expression to its negation.

Given F(w,x,y,z) = xyz'(y'z + x)'+ (w'yz+x'), the complement of F is denoted as F' and can be found by negating the entire function and applying DeMorgan's Law wherever necessary. The steps include negating each variable and operation within the function and switching ANDs to ORs and vice versa.

To find F', we will negate and apply DeMorgan's Law to each part of the function as follows:

1. Negate the entire function: F'(w,x,y,z).
2. Apply DeMorgan's Law to xyz'(y'z + x)', resulting in (x'+y+z)(y+z'+x').
3. Apply the same law to (w'yz+x'), giving us (w+y'+z')(x).
4. The final complement function is then: (x'+y+z)(y+z'+x')(w+y'+z')x.

This process demonstrates the use of DeMorgan's Law to simplify and negate complex Boolean expressions.