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Ch. 2 definitions
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Terms in this set (23)
inductive reasoning
process of reasoning that a rule or statement is true because specific cases are true.
conjecture
a statement you believe is true based on inductive reasoning
counterexample
a statement or reason that proves the conjecture untrue
conditional statement
a statement that can be written in the form "if p, then q"
hypothesis
the part p of a conditional statement following the word if.
conclusion
the part q of a conditional statement following the word then
truth value
either true or false
negation
the part of a statement p is not "not p" or ~p
converse
the statement formed by exchanging the hypothesis and conclusion
inverse
the statement formed by both exchanging and negating the hypothesis and conclusion
contrapositive
the statement formed by both exchanging and negating the hypothesis and conclusion
logically equivalent statements
related conditional statements that have the same truth value
deductive reasoning
the process of using logic to draw conclusions from given facts, definitions, and properties
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
polygon
a closed plane figure formed by three or more line segments
triangle
a three sided polygon
quadrilateral
a four sided polygon
proof
an argument that uses logic,definitions,properties, and previously shown statements to show that a conclusion is true.
theorem
any statement that you can prove.
two-column proof
list the steps of the proof in the left column.
flowchart proof
uses boxes and arrows to show the structure of the proof
paragraph
presents the steps of the proof and their matching reasons as sentences in a paragraph.
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