What is the result of the Boolean expression A AND (B OR C)?

The Boolean expression A AND (B OR C) can be understood through the application of the distributive law of Boolean algebra, which states that A AND (B OR C) is equivalent to (A AND B) OR (A AND C).

In this context, the result can be expressed as A.B + A.C, which means that the output is true if both A and B are true, or if both A and C are true. This formulation aligns perfectly with how logical operations work in digital circuits, allowing the combination of multiple conditions to determine the final output.

The other options do not accurately represent the operation defined in the original expression. For instance, A + B + C implies an OR operation rather than AND, while A.B + B.C suggests a relationship that mixes terms incorrectly, failing to maintain the structure of the original expression. Lastly, A + B.C incorrectly mixes AND and OR operations without adhering to the original logic encapsulated in the expression. Therefore, the correct answer encapsulates the conditions appropriately by using the distributive property of Boolean algebra to demonstrate the relationship outlined in A AND (B OR C).