The Boolean expression $A + A'B$ simplifies to $A + B$. Here's how this works:

Simplification:

1. The given expression is: $A + A'B$

2. Apply the Absorption Law of Boolean algebra, which states: $A + A'B = A + B$ This works because:

   • If $A$ is true, the entire expression $A + A'B$ becomes $A$, as $A$ dominates.
   • If $A$ is false, the term $A'B$ simplifies to $B$.

Hence, the expression is equivalent to $A + B$.

Would you like further details or have additional questions?

Related Questions:

1. What are the key laws of Boolean algebra and how are they applied?
2. Can you provide more examples of simplifications using the Absorption Law?
3. How does the truth table validate the equivalence of $A + A'B$ and $A + B$?
4. Why is Boolean algebra critical in digital logic design?
5. What is the difference between $A + B$ and $AB$ in Boolean expressions?

Tip: Practice truth tables for small Boolean expressions to visualize simplifications.