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argument

a fact or assertion offered as evidence that something is true

conclusion

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

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.)

diagonals

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

premise

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

proof

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

syllogism

deductive reasoning in which a conclusion is derived from two premises

valid argument

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

conditional statement

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

contrapositive

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

converse

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

hypothesis

a proposal intended to explain certain facts or observations

inverse

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

logical chain

A series of rationally linked conditional statements

statement

a fact or assertion offered as evidence that something is true

truth-functionally equivalent

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

compound statement

a statement formed by joining two or more statements

conjunction

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

contradiction

a statement that is the opposite of another statement

disjunction

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

exclusive or

one and only one of the simple sentence is true

inclusive or

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

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

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

conjecture

reasoning that involves the formation of conclusions from incomplete evidence

direct proof

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

theorem

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

two-column proof

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

inductive reasoning

reasoning from detailed facts to general principles

paragraph proof

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

vertical angles

a pair of opposite congruent angles formed by intersecting lines