Question

A) Prove with Boolean algebra the consensus theorem. Give a reason for each step in your proof. (x + y) . (x' + z).(y+ z) = (x + y) .(x' + z)

Part b) Show the dual proof of the part (a)

Answer 1

To prove the consensus theorem in Boolean algebra, we can use the distributive law and the fact that A + B = B + A. By expanding and rearranging the terms, we can show that (x + y) . (x' + z).(y+ z) is equal to (x + y) .(x' + z).

Step-by-step explanation:

To prove the consensus theorem in Boolean algebra, we need to show that (x + y) . (x' + z).(y+ z) is equal to (x + y) .(x' + z). We can do this using the distributive law and the fact that A + B = B + A.

1. Using the distributive law, we can expand (x + y) . (x' + z) as (x . x' + x . z + y . x' + y . z).
2. Applying the fact that A + B = B + A, we can rearrange the terms as (x . x' + y . x' + x . z + y . z).
3. Using the distributive law again, we can factor out x' and z, giving us (x' . (x + y) + z . (x + y)).
4. Finally, we can combine the terms to get (x' + z) . (x + y), which is equal to the right side of the equation.