Because
of the limitations of a standard keyboard we need to adapt some of the
ways things are displayed in the Hurley text. For instance, in
place of the horseshoe we use an arrow (->), in place of the
dot we use the ampersand (&), and in place of the triple bar we use
the arrow pointing in both directions (<->).
Let's say you need to symbolize these sentences:
Logic is easy if the teacher is
kind: K -> E The teacher is kind but logic is
not easy: K & ~E Logic is easy if and only if the
teacher is kind: E <-> K
Please note
that in exams you may use either the symbolization in the Hurley text
or the symbolization I use here.
In presenting an argument form we
separate the premises with commas and we
use the assertibility sign ( |- ) before the conclusion. This
differs from the arrangment in the Hurley text, which has all the
premises above a line and the conclusion below. Note also that
for truth tables we indicate all the variables used in alphabetical
order in front of the form itself.
For using the indirect or reverse method study the following
examples carefully. The idea is that we attempt to force a "bad
line." When that happens we indicate the values of the variables
that allow this. When that would lead to a contradiction (a
roadblock, as it were) we use "x" to show that a particular variable
would have to be both true and false on the same line, and that cannot
happen. Make sure you are comfortable with the basic truth table
assignments, especially when you are working with conditionals.
Go to this page to review these: http://www.internetlogic.org/ttest2.html
Logic is easy only if it is
fun. Logic is fun. Therefore, logic is easy. E -> F, F
|- E E F || E -> F | F | E F
T
T T
F invalid
Logic is easy only if it is
interesting and fun. Logic is easy. Therefore, logic
is interesting.
E F I || E -> (I &
F), E |- I T x
F
T
T T
F valid the point
here is that there is nothing we can supply for "F" that would let the
expression "I & F" be true
