propositional logic

conditionals/hypotheticals

a very common proposition found in arguments. it takes the form:

if p, then q - p and q declarative propositions

also symbolized as p→q

ex. if you are a sister, then you are a sibling

antecedent

“if” clause

consquent

“then” clause

propositions/statements

typically have truth values: conditions that make this statement true

are these two statements the same?

-if i am president, i am a politician (p→q)

-if i am a politician, i am president (q→p)

necessary conditions

the consequent of a condition

ex. if you light a match, then there is enough oxygen in the room. Having enough oxygen is necessary for lighting a match

sufficient

the antecedent of a conditional

ex. if your head is cut off, your life will end. having your head cut off is sufficient for ending your life

if

whatever is after __ is the antecedent

-if you eat lunch, you will feel better

-you will eat better if you eat lunch

only

the exception to the rule that whatever is after “if” is the antecedent when there is an ___ before the if

-only if introduces a necessary condition, not a sufficient one

unless

“x ____ y” means that if y does not occur, then x is sure to occur

ex. you will get wet ____ unless you bring an umbrella (if not-y, then x)