Question

Find the simplified expression A'BC' + AC'.

• A. B
• B. A+C
• C. (A+B)C'
• D. B'C

Hint:

Boolean Simplification. Look for common factors. Apply standard identities, such as the absorption law (\(X + XY = X\)), consensus theorem, or \(X + X'Y = X+Y\).

Answer 1

The Correct Option is C

We need to simplify the Boolean expression \( Y = A'BC' + AC' \)
We can factor out the common term C': $$ Y = C'(A'B + A) $$ Now we use the Boolean algebra identity \( X + X'Y = X + Y \)
In our case, let \(X=A\) and \(Y=B\)
The term inside the parenthesis is \(A + A'B\)
Applying the identity, we get: $$ A + A'B = A + B $$ Substituting this back into the expression for Y: $$ Y = C'(A + B) $$ This is equivalent to \( (A+B)C' \)