Question

The Boolean function \(\overline{P}(\overline{P} + Q)(Q + \overline{Q})\) is equivalent to:

• A. \(P\)
• B. \(\overline{P}\)
• C. \(PQ\)
• D. \(P\overline{Q}\)

Hint:

Remember, \(Q + \overline{Q} = 1\) and \(A(A + B) = A\) are key Boolean simplification identities.

Answer 1

The Correct Option is B

Step 1: Simplify the expression.
Given expression: \[ \overline{P}(\overline{P} + Q)(Q + \overline{Q}) \] Since \(Q + \overline{Q} = 1\), the expression simplifies to \[ \overline{P}(\overline{P} + Q) \]

Step 2: Apply absorption law.
\[ \overline{P}(\overline{P} + Q) = \overline{P} \] since \(\overline{P}\) multiplied by anything containing \(\overline{P}\) results in \(\overline{P}\).

Step 3: Conclusion.
Hence, the Boolean function is equivalent to \(\overline{P}\).