Question

The Boolean function F(x, y) = x'y' + xy' + y(xy') can be simplified to: A) xy' B) y' C) 1 D) x y'

Answer 1

The Boolean function F(x, y) = x'y' + xy' + y(xy') simplifies to 1, as common terms are factored out and Boolean algebra principles are applied to reduce the expression, leading to the answer C) 1.

Step-by-step explanation:

The Boolean function F(x, y) = x'y' + xy' + y(xy') can be simplified by first recognizing that xy' is a common term in the first two terms and that y(xy') simplifies to y since xy' implies that y is true. Therefore, the original equation simplifies to:

• x'y' + xy' + y

Next, we can factor out y' from the first two terms to get:

• y'(x' + x) + y

Since x' + x is always true in boolean algebra, it can be replaced with 1, giving us:

• y'(1) + y

Finally, the parentheses are redundant here, so it further simplifies to:

• y' + y

Again, using the principle of Boolean algebra that y' + y equals 1, we can conclude that the simplified form of the Boolean function F(x, y) is simply:

• C) 1