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, always look for common terms to factor out and apply the distributive property to reduce the complexity.

Answer 1

The Correct Option is A

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. The remaining terms can be simplified using the distributive property of Boolean algebra. After simplifying, the expression becomes \( PQ + R(S + T + U) \).
Step 2: Conclusion.
The correct answer is option (A) because the simplified Boolean expression is \( PQ + R(S + T + U) \).