Question

If the Boolean function \( Z = PQ + PQR + PQRS + PQRST + PQRSTU \), then \( Z \) is:

• A. \( PQ + R(S + T + U) \)
• B. \( PQ \)
• C. \( P + Q \)
• D. \( P + Q + R + S + T + U \)

Hint:

When simplifying Boolean functions, factor out common terms and combine them to simplify the expression.

Answer 1

The Correct Option is C

Step 1: Simplifying the Boolean function.
The given Boolean expression can be simplified by factoring common terms. First, notice that the term \( PQ \) is common to all parts of the function. By applying the distributive property and combining like terms, we get \( Z = P + Q \), which is the simplified form of the original expression.
Step 2: Conclusion.
The correct answer is option (C) because after simplifying, the Boolean function reduces to \( P + Q \).