A two-column proof
uses a visual representation of the logical flow of steps needed to reach a conclusion.
contains a table with a logical series of statements and reasons that reach a conclusion.
contains a set of sentences explaining the steps needed to reach a conclusion.
uses inductive reasoning to prove a statement.
uses a formal structure with numbered statements and corresponding reasons.
A two-column proof is a type of proof that contains a table with a logical series of statements and reasons that lead to a conclusion. It is called a "two-column" proof because it is divided into two columns: the left column contains the logical series of statements, while the right column provides the corresponding reasons for each statement.
Unlike a visual representation, a two-column proof does not use diagrams or visual aids to illustrate the logical flow of the steps. Instead, it uses sentences and statements to explain each step and how it relates to the overall conclusion.
In contrast to inductive reasoning, which involves making generalizations based on specific observations or patterns, a two-column proof typically uses deductive reasoning. Deductive reasoning starts with a set of premises or assumptions and uses logical principles or rules of inference to derive a conclusion that necessarily follows from those premises or assumptions.