two-valued logic

every statement is either True or False

truth table

used to determine the truth or falsity of a complicated statement based on the truth or falsity of its simple components

conjunction

"and"; true when both statements are true; ^

disjunction

"or"; true when @ least 1 statement is true, V

negation

"not", ~

inclusive "or"

doing 1/other/both

when is p → q not true?

when p is true and q is false

tautology

rule of logic

a formula which is "always true" - all the end results are true

p ⇔ q

p iff q

both p & q r equivalent. true if p & q r both true/both false

contradiction

opposite of a tautology, a formula which is "always false"

what r p &q called in p ⇒ q?

p = hypothesis

q = conclusion

p ⇒q

if p, then q

p implies q

p if q

4 ways to rewrite a statement

1) if p, then q

2) Every p has q.

3) The fact that p, implies that q

4) p iff/if/only if q

converse

q ⇒ p

inverse

~p ⇒ ~q

contrapositive

~q ⇒ ~p

Direct Argument

p ⇒ q

p

...q

premise

a statement that is assumed to be true

a given statement in an argument. the resulting statement is called the conclusion

Indirect Argument

p ⇒ q

~q

... ~p

Chain Rule

p ⇒ q

q ⇒ r

...p ⇒ r

Or Rule

p V q

~p

...q

p V q

~q

...p

good definition

built from a true conditional with a true converse

invalid argument

argument that doesn't use rules of logic

4 rules of biconditionals

p ⇔ q

p

... q

p ⇔ q

q

... p

p ⇔ q

~p

... ~q

p ⇔ q

~q

... ~p

Venn diagram placement for conditionals/implications

two-column proof

a proof written in 2 columns

statements r listed in 1 column & justifications r listed in the other column

paragraph proof

a proof whose statements & justifications r written in paragraph form

flow proof

a proof written as a diagram using arrows to show the connections b/w statements

#'s written over the arrows refer to a #-ed list of the justifications 4 the statements

postulate

a statement assumed to be true w/out proof

Addition Property of Equality

If the same # is added to equal #'s, the sums r equal

a = b → a + c = b + c