Chapter 2 Flashcards
Algebraic proof
A proof made up of a series of algebraic statements.
Axiom
Postulate–a statement that is accepted as true without proof
Compound statement
Two or more statements joined by the words and or or
Conclusion
The phrase immediately following the word then
Conditional statement
Is a statement that can be written in the if-then form
Conjecture
A concluding statement reached using inductive reasoning
Conjunction
A compound statement using the word and
Contrapositive
Formed by negating both the hypothesis and the conclusion of the converse of the conditional
Converse
Formed by exchanging the hypothesis and the conclusion of the conditional
Counter example
A false example that is a number drawing or example
Deductive argument
Created by forming a logical chain of statements linking the give to what you are trying to prove
Deductive reasoning
Uses facts rules definitions or properties to reach logical conclusions from given statements
Disjunction
A compound statement that uses the word or
Formal proof
Contains statements and reasons organized into two columns
Hypothesis
The phrase immediately following the word if
If then statement
The form of if P then Q
Inductive reasoning
Reasoning that uses a number of specific examples to arrive at a conclusion
Informal proof
Involves writing a paragraph to explain why a conjecture for a given situation is true
Inverse
Formed by negating both the hypothesis and the conclusion of the conditional
Logically equivalent
Statements with the same truth values
Negation
The opposite meaning of a statement and opposite truth value
Postulate
A statement that is 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
Other statements that are based on a given conditional statement
Theorem
A statement or conjecture that has been proven and can be used as a reason to justify statements in other proofs
Truth table
A convenient method for organizing the truth of statements
Truth value
Either true or false
Two column proof
Contains statements and reasons organized in two columns
Biconditional
When the conditional and converse are true
