We begin with sentential logic, which deals with the logical
connections between whole sentences.  The only symbols we need concern
ourselves with in sentential logic are ~, &, v, ->, and <->.  We will not
discuss =, /\, and \/ until we get to predicate logic, which deals with the
logical connections between subjects and predicates in sentences.

        In this post, I will introduce the use of ~, &, v, -> and <->.  We
use these symbols, or similar symbols, to make logical claims about the
truth or falsehood of sentences, which we represent by single letters.  For
instance, we could let P stand for 'Peter picked a pickled pepper.'  In
this case, ~P would mean 'Peter did not pick a pickled pepper.'  If we let
Q mean 'Jack jumped over the candle stick,' then (P & Q) would mean 'Peter
picked a picked pepper, and Jack jumped over the candle stick."  (P v Q)
would mean 'Either Peter picked a pickled pepper, or Jack jumped over the
candle stick."  (P -> Q) would mean "If Peter picked a pickled pepper, then
Jack jumped over the candle stick."  (P <-> Q) would mean 'Peter picked a
pickled pepper if and only if Jack jumped over the candle stick."  If you
have any questions about what I have written, please ask them. After I have
answered any questions, I will go on to describe the meanings of these
symbols in more detail.  For the moment, please limit your questions to ~,
&, v, -> and <->.  I will discuss the other symbols in due time.