Wednesday 28 November

Valid Arguments

An argument consists of a premise and a conclusion.
If the truth table for an argument leads to a tautology, then the argument is valid.
Example:
Consider the following propositions…:
p: It rains
q: You stay indoors
And their negations:
¬p: It does not rain
¬q: You do not stay indoors
From these propositions I have constructed the following argument:
If it rains then you stay indoors.
It does not rain.
             Therefore, you do not stay indoors.
”If it rains then you stay indoors.
It does not rain”. – The premise.
            ”Therefore, you do not stay indoors.” – The conclusion.
The argument in symbols:
p \implies q
¬p
———————
¬q
What we need to show in a truth table is:
(p \implies q) ∧ ¬p \implies ¬q
to state whether it is a valid argument or not.
 P. 255, review set 8B, 7a. Then logic examination questions or revision exercises.