| A | B |
|---|
| biconditional statement | "p if and only if q" which is also written as p <==> q |
| conclusion | The "then" phrase of a conditional statement, or q |
| conditional statement | "if p, then q" which is also written as p ==> q |
| contrapositive | A conditional statement where p ==> q is ~ q ==> ~ p; it is true if and only if the conditional statement is true |
| converse | Formed by interchanging the hypothesis and the conclusion of a conditional statement, or q ==> p |
| corollary | A theorem that follows easily from a previously proved theorem |
| counterexample | An example of a conditional statemet in which the hypothesis is fulfilled and the conclusion is not fulfilled, proving the statement false |
| deductive reasoning | Using the laws of logic to prove statements (theorems) from known statements (postulates and previously proved theorems) |
| hypothesis | The "if" phrase of a conditional statement, or p |
| indirect proof | A proof where of all possible cases, all but one is impossible which allows the conclusion that the remaining case must be true (proof by contradiction) |
| inductive reasoning | Making a conjecture about several examples after looking for a pattern in the examples |
| Law of Detachment | If p ==> q is a true conditional statement, and p is true, then q is true |
| Law of Syllogism | If p ==> q and q ==> r are true conditional statements, then p ==> r is also true |
| negation of a statement | The denial of a statement, as in p and the denial ~p |
| postulate | A statement that is accepted as true without proof |
| proof | An organized series of statements that show the statement to be proved follows logically from known facts (given statements, postulates, and previously proven theorems) |
| theorem | A statement that must be proved to be true |
