Question

Simplify the equation using Boolean algebra properties.

Simplify (x'z'+x'z)+yz' to x'+z'y
Select a property from the right to apply
(x'z'+x'z)+yz':
Properties
a. Distributive
b. Commutative
c. Complement
d. Identity
e. Null elements
f. Idempotence

Answer 1

The expression (x'z' + x'z) + yz' simplifies to x' + yz' using the distributive and complement properties of Boolean algebra.

Step-by-step explanation:

To simplify the Boolean expression (x'z' + x'z) + yz', we will apply the distributive property and then the idempotence property of Boolean algebra.

First, let's apply the distributive property to x'z' + x'z, which is similar to the distributive property (A(B + C) = AB + AC) in normal algebra:

x'z' + x'z = x'(z' + z) = x' because z' + z is 1 due to the complement property.

Now, we can substitute x' back into the original expression:

(x'z' + x'z) + yz' becomes x' + yz'.

The expression x' + yz' is already in its simplest form according to Boolean algebra; therefore, the simplified expression is x' + yz'.

We have thus used the distributive property to simplify the first part of the expression, and then we recognized that the expression was already simplified.