Question

The simultaneous equations on the Boolean variables x, y, z, and w are: x + y + z = 1, xy = 0, x + y + w = 1, xy + z = 0. The solution for x, y, z, and w, respectively, is:

• A. 0100
• B. 1011
• C. 1000
• D. 1101

Hint:

Translate Boolean equations into logical constraints to systematically solve for each variable.

Answer 1

The Correct Option is A

The following equations are presented: 1. x + y + z = 1, which signifies that at least one of x, y, z is 1. 2. xy = 0, indicating that at least one of x or y is 0. 3. x + y + w = 1, which signifies that at least one of x, y, w is 1. 4. xy + z = 0. Given xy = 0, it is concluded that z = 1. Solving these equations leads to the values x = 0, y = 1, z = 0, w = 0. The resulting solution is 0100.