Question

The Boolean expression $(AB)(\bar{A}+B)(A+\bar{B})$ can be simplified to

• A. $A+B$
• B. $\bar{A}B$
• C. $A+\bar{B}$
• D. $AB$

Hint:

When simplifying Boolean expressions, always check for annihilation identities like $A\bar{A}=0$ and $BB=B$.

Answer 1

The Correct Option is C

Step 1: Expand the expression.
$(AB)(\bar{A}+B)(A+\bar{B})$ First multiply $(AB)(\bar{A}+B)$: $AB\bar{A} + AB\cdot B = 0 + AB = AB.$

Step 2: Multiply the remaining factor.
Now the expression becomes $AB(A+\bar{B}) = ABA + AB\bar{B}.$

Step 3: Simplify.
$ABA = AB,$ $AB\bar{B}=0.$ Thus total expression = $AB.$

Step 4: Conclusion.
The simplified Boolean expression is $AB.$