What is the set of rules and theorems used to express and solve logical operations?

The set of rules and theorems used to express and solve logical operations is known as Boolean algebra. This mathematical framework is fundamental in computer science, particularly in the design and simplification of digital circuits.

Boolean algebra operates on binary values (true and false, often represented as 1 and 0) and includes various operations such as AND, OR, and NOT. It allows for the structuring of logical statements and the simplification of complex logical expressions, making it essential for creating efficient algorithms and circuit designs in computing.

Other areas, while related in the broader context of mathematics and logic, do not specifically focus on the operations and expressions pertinent to logical operations in the same manner. Logic gates represent physical implementations of logical operations but do not constitute a formal set of rules or theorems. Set theory deals primarily with collections of objects and their relationships, while mathematical logic encompasses broader areas including proofs and formal reasoning, rather than specifically focusing on logical operations like Boolean algebra does.

This precision in focusing on logical operations distinguishes Boolean algebra as the correct answer.