-~------~-~~Chapter 1: Propositions and Predicates );! 29
EXAMPLE 1.31
Test the validity of the following argument:
If I get the notes and study well, then I will get first class.
I didn't get first class.
So either I didn't get the notes or I didn't study well.
Solution
Let P denote '1 get the notes'.
Let Q denote 'I study well'.
Let R denote '1 will get first class.'
Let S denote 'I didn't get first class.'
The given premises are:
(i) P ;\ Q =:} R
(ii) -, R
The conclusion is -, P v -, Q.
l.P;\Q=:}R
2. -, R
3. -, (P ;\ Q)
4. -,P v-,Q
Thus the argument is valid.
EXAMPLE 1.32
Premise (i)
Premi se (ii)
Lines I, 2 and modus tollens.
DeMorgan's law
Explain (a) the conditional proof rule and (b) the indirect proof.
Solution
(a) If we want to prove A =:} B, then we take A as a premise and construct
a proof of B. This is called the conditional proof rule. It is denoted
by CPo
(b) To prove a formula 0:, we construct a proof of -, 0: =:} F. In
particular. to prove A =:} B. we construct a proof of A ;\ -, B =:} F.
EXAMPLE 1.33
Test the validity of the following argument:
Babies are illogical.
Nobody is despised who can manage a crocodile.
Illogical persons are despised.
Therefore babies cannot manage crocodiles.
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