Question

The Boolean expression for the following truth table is:

 

• A. \( F = x'y'z + xy'z + x'y'z' \)
• B. \( F = x'y'z' + xy'z + xyz' \)
• C. \( F = x'y'z + xy'z + xyz \)
• D. None of these

Hint:

Always verify Boolean expressions by comparing with actual minterms from the truth table and simplifying logically.

Answer 1

The Correct Option is D

Step 1: Identify rows where \( f = 1 \)
From the table, \( f = 1 \) for:
(0,1,0) → \( x'y z' \)
(0,1,1) → \( x'y z \)
(1,0,0) → \( x y' z' \)
(1,1,0) → \( x y z' \)
So, \[ F = x'y z' + x'y z + x y' z' + x y z' = x'y + x z' \quad ({as simplified expression}) \] Step 2: Check options
None of the given options match this simplified expression. Hence: