Consider the following Boolean expression: F(A, B, C, D) = (A + B) (B' + C + D') (A + C + D') (B + D') (C + D')
To eliminate as many terms as possible using the Consensus Theorem, we need to identify pairs of terms that differ in only one variable. Let's examine the expression:
(A + B) (B' + C + D') (A + C + D') (B + D') (C + D')
First, let's look at the terms (A + B) and (A + C + D'). These two terms differ in the variable B. We can eliminate the variable B by applying the Consensus Theorem:
(A + B) (A + C + D') = A + C + D'
Next, let's consider the terms (B' + C + D') and (B + D'). These two terms differ in the variable C. We can eliminate the variable C by applying the Consensus Theorem:
(B' + C + D') (B + D') = B' + D'
Finally, let's examine the terms (A + C + D') and (C + D'). These two terms differ in the variable A. We can eliminate the variable A by applying the Consensus Theorem:
(A + C + D') (C + D') = C + D'
After applying the Consensus Theorem to eliminate as many terms as possible, the simplified Boolean expression becomes:
F(A, B, C, D) = A + C + D' (B' + D') (C + D')
Please note that there may be additional simplifications possible depending on the specific requirements or context of the problem.