2.5 Valid Arguments
Argument is made up of premises that lead to a conclusion.
A mathematical argument assumes that the premise is always true. Logic is not concerned with whether the premises are true or false, but rather with what can be validly inferred from them.
Ex 1 “Emus cannot fly. Jane is an emu.” What is the conclusion here?
The form of this argument is 
. Everything above the line is a premise. The conclusion is below the line.
Ex 2 p: x is a positive integer, q: 
.
Is this a valid argument? 
Write down the known truth values starting with p then q. Then fill out the rest as
needed.
|
p |
q |
|
|
|
|
T T F F |
T F T F |
T F T T |
T F T F |
T T F T |
Since the end result is not a tautology, the argument is invalid.
Ex 3 
valid argument?
|
p |
q |
|
|
|
|
|
|
T T F F |
T F T F |
F F T T |
F T F T |
T F T T |
F F F T |
T T T T |
Valid argument.
Ex 4 
valid argument?
p. 512# 1-6
p. 514# 1-4