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Arts and Humanities
Philosophy
Logic
Chapter 2 Geometry
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Gravity
Rhonda 2-0,2-5
Terms in this set (34)
Inductive Reasoning
Reasoning That assumes that the conclusion is false and then shows that this assumption leads to a contradiction of the hypothesis like a postulate, theorem, or corollary. Then,since the assumption has been proved false, the conclusion must be true.
Conjecture
An educated guess based on known information.
Statement
Any sentence that is either true or false, but not both.
Truth value
The truth or falsity of a statement
Negation
If a statement is represented by p, then not p is the negation of the statement.
Compound Statement
A statement formed by joining two or more statements.
Conjunction
and
Disjunction
or
Truth Table
A table used as a convenient method for organizing the truth values of statements.
Theorem
A statement or connection that can be proven the by undefined terms, definitions, and postulates.
Related Conditionals
Statement that are based on a given conditional statement.
Postulate
A statement that describes a fundamental relationship between the basic terms of geometry. Postulates are 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.
Paragraph proof
An informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true.
Law of Detachment
If p---->q is a true conditional and p is true, then q is also true.
Law of Syllogism
If ----> q and q----> r are true conditionals, then p---> r is also true.
Logically equivalent
Statements that have the same truth values.
Inverse
The statement formed by negating both the hypothesis and conclusion of a conditional statement.
Informal proof
A paragraph proof.
If-Then statement
A compound statement of the form "if p, then q," where p and q are statements.
Hypothesis
In a conditional statement, the statement that immediately follows the word if.
Deductive Reasoning
A system of reasoning that uses facts, rules, definitions,or properties to reach logical conclusions.
Deductive Argument
A proof formed by a group of algebraic steps used to solve a problem.
Converse
The Statement formed by exchanging the hypothesis and conclusion of a conditional statement.
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.
Contrapositive
The Statement formed by negating both the hypothesis and conclusion of a conditional statement.
Axiom
A Statement that is accepted as true.
Valid
is not logically correct.
two-column proof
a formal proof that contains statements and reasons organized in two columns. Each step is called a statement, and the properties that justify each step are called.
figure numbers
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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
Counter example
an example used to show that a given statement is not always true
formal proof
a two-column proof containing statement and reasons
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