How can we help?

You can also find more resources in our Help Center.

law of syllogism

if p ➡q and q➡r are true conditional statements then p➡r is true

biconditional statement

a statement that contains the phrase "if and only if" the symbol for "if and only if" is ↔

theorem

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

equivalent statement

two statements that are both true of both false

line perpendicular to a plane

a line that intersects the plane in in a point and is perpendicular to every line in the plane that intersects it

converse

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

hypothesis

the "if" part of a conditional statement

conditional statement

has two parts, a hypothesis and a conclusion.

two-column proof

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

conclusion

the "then" part of a conditional statement

perpendicular lines

two lines that intersect to form a right angle. the smybol for "is perpendicular to" is ⊥

negation

the negative of a statement. the negation symbol is ~

law of detachment

if p ➡ q is a true conditional statement and p is true, than q is true

paragraph proof

a type of proof written in paragraph form

if-then form

the "if" part contains the hypothesis and the "then" part contains the conclusion.

logical argument

an argument based on deductive reasoning, which uses facts, definitions, and accepted properties in a logical order

contrapositive

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

inverse

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