Logical notation

simple sentence

does not contain any logical connections (and/or/if, then/not)

negation

the opposite. represented by -

Or (inclusive)

true if at least one is true. V

compound sentence

contains multiple logical operators

when to use parenthesis

to remove ambiguity with multiple operators

and/conjection

^, true only when all parts are true

if/then

if the first is true, then the second must be true. =>

biconditional (if, and only if)

if one is true, the other is true. If one is false, the other is false <=>

Truth tables

column for each simple sentence, another for additional complex expression, fill in all possible values then go left to right using previous columns

when is a conditional true

a conditional is true if the antecedent is true, and the consequence is true, or if the antecedent is true