********
* remember:
* no CS 100 lecture this FRIDAY, October 12
* that's why HOMEWORK 6's paper is due
11:00 am on MONDAY, October 15
********
* ONE MORE EXAMPLE:
* If the Green Party loses in the local election, then the
developer-friendly politicians will have a majority in the
city council.
* If the developer-friendly politicians have a majority in the
city council, then the city council will vote down
restrictions on development on agricultural land.
* It is NOT the case that the city council will vote down
restrictions on development on agricultural land OR
that the Green Party will lose in the local election.
* THEREFORE, it is NOT the case that IF the Green Party does
NOT lose in the local election, THEN the city council will
NOT vote down restrictions on development of agricultural
land.
* IDENTIFY the simple statements in the argument, and give
each a letter
P = the Green Party loses in the local election
Q = the developer-friendly politicians will have a majority
in the city council
R = the city council will vote down
restrictions on development on agricultural land
* now rewrite the argument in prop logic form:
P -> Q
Q -> R
~(R v P)
∴ ~( ~P -> ~R )
* make a TRUTH TABLE for this argument,
and MARK the columns that represent the premise(s)
and conclusion:
(*) (*) (*) (C)
P Q R P->Q Q->R RvP ~(RvP) ~P ~R ~P->~R ~(~P->~R)
------------------------------------------------------------
T T T T T T F F F T F
T T F T F T F F T T F
T F T F T T F F F T F
T F F F T T F F T T F
F T T T T T F T F F T
F T F T F F T T T T F
F F T T T T F T F F T
F F F T T F T T T T F
...and, as shown on document camera,
when we cross out all the rows where any premise
is F,
there is only 1 row left where all 3 premises
are true,
and in THAT the Conclusion is false,
SO: this argument is NOT valid
(all of its premises being true does NOT
guarantee that its conclusion is true)
* NEXT: a little programming!
with WeScheme
(www.wescheme.org)