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argument

a fact or assertion offered as evidence that something is true

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conclusion

the proposition arrived at by logical reasoning (such as the proposition that must follow from the major and minor premises of a syllogism)

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deductive reasoning

reasoning in which a conclusion is reached by stating a general principle and then applying that principle to a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.)

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diagonals

a segment that connects two vertices that are not next to each other

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premise

a statement that is assumed to be true and from which a conclusion can be drawn

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proof

a formal series of statements showing that if one thing is true something else necessarily follows from it

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syllogism

deductive reasoning in which a conclusion is derived from two premises

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valid argument

an argument in which the reasons support the conclusion so that the conclusion follows from the reasons offered.

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conditional statement

a type of logical statement that has two parts, a hypothesis and a conclusion

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contrapositive

the statement formed when you negate the hypothesis and conclusion of the converse of a conditional statement

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converse

the statement formed by switching the hypothesis and conclusion of a conditional statement

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hypothesis

a proposal intended to explain certain facts or observations

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inverse

the statement formed when you negate the hypothesis and conclusion of a conditional statement

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logical chain

A series of rationally linked conditional statements

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statement

a fact or assertion offered as evidence that something is true

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truth-functionally equivalent

for every combination of truth values that we make, these expressions will yield the same truth value

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compound statement

a statement formed by joining two or more statements

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conjunction

a compound statement formed by joining two or more statements with the word and

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contradiction

a statement that is the opposite of another statement

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disjunction

a compound statement formed by joining two or more statements with the word or

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exclusive or

one and only one of the simple sentence is true

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inclusive or

one or both of the simple sentence are true(the one word that we use)

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indirect proof

a type of proof where it is first assumed that the statement is false. If the assumption leads to an impossibility, than the original statement has to be proven true

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proof by contradiction

a form of proof that establishes the truth or validity of a proposition by showing that the proposition being false would imply a contradiction

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conjecture

reasoning that involves the formation of conclusions from incomplete evidence

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direct proof

a proof that starts with the given statements and uses the laws of logic to arrive at the statement to be proved

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theorem

a true statement that follows as a result of other true statements

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two-column proof

a type of proof written as numbered statements and reasons that show the logical order of an argument

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inductive reasoning

reasoning from detailed facts to general principles

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paragraph proof

an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true

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vertical angles

a pair of opposite congruent angles formed by intersecting lines

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