The last line of a proof represents the given information. the argument. the conclusion. the assumptions.
The Correct Answer and Explanation is:
Correct Answer: The conclusion.
In a mathematical or logical proof, the last line represents the conclusion. This is the final statement that the proof establishes as true, based on the logical progression of statements leading up to it. Proofs typically start with given information (also called premises or assumptions) and apply rules of logic, definitions, theorems, or previously established results to reach a new statement, ultimately ending in the conclusion.
Explanation:
To understand why the last line is the conclusion, it’s important to look at the structure of a proof. A formal proof is a logical argument that demonstrates the truth of a mathematical statement. It begins with what is given or assumed to be true. These are the starting points or axioms. From these starting points, one applies logical reasoning and valid inference rules to derive new truths step by step.
Each line in the proof builds upon previous ones, showing a clear logical progression. The goal of the proof is to arrive at the statement you want to prove—this is the conclusion. It appears as the final step in the sequence because it is the end result of all the reasoning.
For example, in a two-column proof in geometry, the left column lists statements and the right column lists reasons. The last row of this table contains the final statement being proven, supported by all previous steps. Similarly, in a paragraph or flowchart proof, the last sentence expresses the conclusion drawn from the reasoning provided.
To summarize, the last line of a proof is not the assumptions, argument, or given information, but rather the logical end-point—the conclusion that the entire proof is designed to demonstrate.
