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Chapter 2 Definitions
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Key Concepts:
Terms in this set (27)
inductive reasoning
The process of reasoning that a rule or statement is true because specific cases are true.
conjecture
A statement that is believed to be true.
counterexample
An example that proves that a conjecture or statement is false.
conditional statement
A statement that can be written in the form "if p, then q," where p is the hypothesis and q is the conclusion.
hypothesis
The part of a conditional statement following the word "if".
conclusion
The part of a conditional statement following the word "then".
truth value
A statement can have a truth value of true (T) or false (F).
negation
The negation of statement "p" is "not p", written as ~p.
converse
The statement formed by exchanging the hypothesis and conclusion of a conditional statement.
inverse
The statement formed by negating the hypothesis and conclusion of a conditional statement.
contrapositive
The statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement.
logically equivalent statements
Statements that have the same truth value.
deductive reasoning
The process of using logic to draw conclusions.
biconditional statement
A statement that can be written in the form "p if and only if q".
definition
A statement that describes a mathematical object and can be written as a true biconditional statement.
polygon
A closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear.
triangle
A three-sided polygon.
quadrilateral
A four-sided polygon.
proof
An argument that uses logic to show that a conclusion is true.
theorem
A statement that has been proven.
two-column proof
A style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column.
flowchart proof
A style of proof that uses boxes and arrows to show the structure of the proof.
paragraph proof
A style of proof in which the statements and reasons are presented in paragraph form.
compound statement
Two statements that are connected by the words "and" or "or".
conjunction
A compound statement that uses the word "and".
disjunction
A compound statement that uses the word "or".
truth table
A table that lists all possible combinations of truth values for a statement and its components.
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