In Boolean algebra, AB + AC equals which property?

In Boolean algebra, AB + AC equals which property?

• A. Commutative Property
• B. Associative Property
• C. Identity Property
• D. Distributive Property

Answer: (D)

Distributive property at work here shows how a common factor can be factored from a sum of products. AB + AC has the common term A, so you can factor it to A(B + C). This is the distributive law in reverse: AND distributes over OR. Interpreting it in logic terms, if A is true and either B or C is true, then AB + AC is true, which is exactly A AND (B OR C). This kind of step is key for simplifying expressions and designing more efficient circuits, because it can reduce the number of gates used. It isn’t about swapping order (commutative), regrouping (associative), or using a neutral element (identity).

Distributive property at work here shows how a common factor can be factored from a sum of products. AB + AC has the common term A, so you can factor it to A(B + C). This is the distributive law in reverse: AND distributes over OR. Interpreting it in logic terms, if A is true and either B or C is true, then AB + AC is true, which is exactly A AND (B OR C). This kind of step is key for simplifying expressions and designing more efficient circuits, because it can reduce the number of gates used. It isn’t about swapping order (commutative), regrouping (associative), or using a neutral element (identity).