v is the or symbol.
~ is the not symbol.
-> is the implies symbol.
the or statement is ~p v q
the implies statement is ~q -> (~p v q)
the or statement is only false if both ~p and q are false.
the implies statement is only false if ~q is true and (~p v q) is false.
there are 4 possible conditions in the truth table because there are 2 variables involved. those variables are p and q. the possible conditions are 2 * 2 (2 possible conditions for each variable used).
