math terms- chapter two, page two

Laws of Detachment

When P implies Q is true and P is true, then Q must be true

Logic

The study of reasoning

Logical Equivalents

Two statements are logically equivalent if they always have the same truth value

Mathematical Sentences

a sentence that contains a complete thought and can be judged true or false

Negation

a statement that has the opposite truth value of a given statement

Open sentence

any sentence that contains a variable

phrase

an expression that is only part of a sentence

premise/ antecedent

an assertion that begins an argument. the hypothesis usually follows the word if

solution set/ truth set

the set of all replacements that will change an open sentence to a truth sentence

statement/ closed sentence

a sentence that can be judged true or false

tree diagram

show all possible combinations f truth values p and q

tautology

a statement that is always true

truth table

a summary of all possible truth values of a logic statement

truth value

either true or false

valid argument

uses of series of statement called premises that have known truth values to arrive at a conclusion