Question

Simplify the Boolean expression \[ ab'+bc+ac \]

• A. \(ab'+bc\)
• B. \(ab'+ac\)
• C. \(bc+ac\)
• D. \(a+b+c\)

Hint:

Consensus theorem: \[ XY+X'Z+YZ=XY+X'Z \] helps remove redundant terms quickly.

Answer 1

The Correct Option is A

Concept: Use the consensus theorem \[ XY+X'Z+YZ=XY+X'Z. \]

Step 1: Identify terms.
\[ ab'+bc+ac \] contains \[ ab',\quad bc,\quad ac. \]

Step 2: Apply consensus theorem.
The term \[ ac \] is redundant. Therefore \[ ab'+bc+ac=ab'+bc. \]

Step 3: Write simplified expression.
\[ \boxed{ab'+bc} \]