Math: Chapter 2 - Reasoning and Proof
Algebraic proof: A proof that is made up of a series of algebraic statements.
The properties of equality provide justification for many statements In algebraic proofs.
Compound statement: a statement formed by joining 2 or more statements
Conclusion: in a conditional statement, the statement that immediately follows the word then
Conditional statement: A statement that can be written in if-then form
Conjecture: An educated guess based on known info
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 2 or more statements with the word “or”
A 2-column proof containing statements and reasons: Formal proof
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 a number of specific examples to arrive at a plausible generalization or prediction.
Conclusions arrived at by inductive reasoning lack the logical certainty of those arrived at by deductive reasoning
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
Formula of Law of Detachment: if p —> q is a true statement and p is true then q is true
deductive reasoning
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
Formula of the Law of Syllogism: if p —> q and q —> r are true statements, the p —> r is a true statement
deductive reasoning
Logically equivalent: statements that have the same truth values
Negation: If a statement is represented by p, then not p is the negation of the statement
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 you make is supported by a statement that is 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 postulated
Truth value: the truth or falsity of a statement
Two-column proof: a formal proof that contains statements and reasons organized in two columns