Question

Using the basic identities of Boolean algebra, show that: xy + x'z + yz = xy + x'z

Answer 1

To prove the given expression xy + x'z + yz = xy + x'z, we apply the consensus theorem in Boolean algebra, simplifying the expression by removing the yz term which is redundant, resulting in the simplified expression xy + x'z.

Step-by-step explanation:

To prove the given Boolean expression xy + x'z + yz = xy + x'z, we can use the consensus theorem which states that AB + A'C + BC = AB + A'C. We can map our variables to the theorem where A maps to x, B to y, and C to z. Thus, we substitute x for A, y for B, and z for C into the consensus theorem to apply it to our given expression.

Now the original expression xy + x'z + yz can be simplified using the consensus theorem:

1. Remove the yz term because it is implied by the presence of xy and x'z, which cover all possible values for y and z when combined.
2. Therefore, we are left with xy + x'z as the simplified expression.

This proves that the given Boolean expression simplifies according to the basic identities of Boolean algebra.