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