Math: Chapter 2 - Reasoning and Proof

Algebraic proof

A proof that consists of a series of algebraic statements.

Properties of equality

Justifications for statements in algebraic proofs.

Compound statement

A statement formed by combining two or more statements.

Conclusion

The statement that immediately follows the word "then" in a conditional statement.

Conditional statement

A statement that can be written in if-then form.

Conjecture

An educated guess based on known information.

Conjunction

A compound statement formed by joining two or more statements with the word "and."

Contrapositive

The statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.

Converse

The statement formed by exchanging the hypothesis and conclusion of a conditional statement.

Counterexample

An example used to show that a given statement is not always true.

Deductive reasoning

A system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions.

Disjunction

A compound statement formed by joining two or more statements with the word "or."

Two-column proof

A formal proof that contains statements and reasons organized in two columns.

Hypothesis

In a conditional statement, the statement that immediately follows the word "if."

If-then statement

A compound statement of the form "if p, then q," where p and q are statements.

Inductive reasoning

Reasoning that uses specific examples to arrive at a plausible generalization or prediction.

Inverse

The statement formed by negating both the hypothesis and conclusion of a conditional statement.

Law of Detachment

Uses facts, rules, definitions, or properties to reach logical conclusions from given statements.

Law of Syllogism

Allows you to draw conclusions from two true conditional statements when the conclusion of one statement is the hypothesis of the other.

Logically equivalent

Statements that have the same truth values.

Negation

The negation of a statement represented by p is "not p."

Paragraph proof

An informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true.

Postulate

A statement that describes a fundamental relationship between the basic terms of geometry, accepted as true without proof.

Proof

A logical argument in which each statement is supported by a statement accepted as true.

Related conditionals

Statements that are based on a given conditional statement.

Statement

Any sentence that is either true or false, but not both.

Theorem

A statement or conjecture that can be proven true by undefined terms, definitions, and postulates.

Truth value

The truth or falsity of a statement.