What is a term that is true in one part of an expression will be true in all parts of the expression?

The Law of Identity states that if a particular property is true for one part of an expression, it must also hold true for the entire expression. This principle is fundamental in mathematics and logic, as it asserts that an element is identical to itself, and thus maintains its properties consistently throughout any logical or mathematical constructs. In practical terms, if 'A' is true, then 'A' is true everywhere it appears, which applies not only in logical arguments but also in equations and algebraic expressions.

In contrast, the other concepts provided serve different functions within logic and mathematics. The Law of Contradiction asserts that contradictory statements cannot both be true in the same context. The Law of Excluded Middle deals with binary truth values, indicating that statements are either true or false, with no middle ground. The Law of Distribution pertains to how multiplication distributes over addition in algebra. Each of these laws plays a significant role in logic and mathematics, but they do not encapsulate the idea of a property being true in one segment and thus true in all segments as the Law of Identity does.