GNED 1101 Chapter Notes - Chapter 1.6-1.7: Fallacy, Contraposition
22 May 2018
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1.6 Negatios of Coditioal Stateets De Morga’s Law
The Negation of the Conditional Statement PQ
The egatio of a oditioal stateet is doe y egatig the oseuet ad sithig to the ad
connective
o Thus the negation of P Q is P Q
P
Q
P Q
Q
P Q
T
T
T
F
F
T
F
F
T
T
F
F
T
F
F
F
F
T
T
F
P Q and P Q have the opposite truth values so P Q negates PQ
This can be expressed as (pq) p q
Thus the negation of the conditional p q is p q
De Moga’s La
He concluded that
o (p q) p q
o (p q) p q
In a table both statements of each version have the same truth value, thus making them equivalent statemnets
. Thus the statement has the same value as its negated version
In negation the Conjunction , change the conjunction to a disjunction
o (pq) p q
In negating the disjunction , change the disjunction to a conjunction
o (pq) p q
1.7 Arguments and Truth Tables
Defining valid arguments
An argument consists of two parts
o The given statements are the premises
o The conclusion
An argument is valid if the conclusion is true whenever the premises are assumed to be true
An argument that is not valid is said to be an invalid argument or a fallacy
An argument p q can be represented
eaig theefoe
To decide whether this argument is valid, we rewrite it as a conditional statement that has the following form
[(p q) p] q
Where (pq) is premise 1, and p is premise 2, and q the conclusion
To find out If the conjunctions premises implie that the conclusion is true we need to construct a
truth table
P Q
pq
[(pq) p)
[(pq) p] q
T T
T
T
T
T F
F
F
T
F T
T
F
T
F F
T
F
T
Because the statement overall is true in every case it is a tautology. This means that the premises imply the
conclusion. Therefore the argument is valid. Thus if an argument is a tautology it is valid
Thus p
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q is direct reasoning. All arguemnets that have direct reasoning are valid
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Document Summary
1. 6 negatio(cid:374)s of co(cid:374)ditio(cid:374)al state(cid:373)e(cid:374)ts (cid:894)de morga(cid:374)"s law(cid:895) The (cid:374)egatio(cid:374) of a (cid:272)o(cid:374)ditio(cid:374)al state(cid:373)e(cid:374)t is do(cid:374)e (cid:271)y (cid:374)egati(cid:374)g the (cid:272)o(cid:374)se(cid:395)ue(cid:374)t a(cid:374)d s(cid:449)it(cid:272)hi(cid:374)g to the (cid:862)a(cid:374)d(cid:863) connective. Thus the negation of p q is p q. P q and p q have the opposite truth values so p q negates p q. This can be expressed as (p q) p q. Thus the negation of the conditional p q is p q. He concluded that: (p q) p q, (p q) p q. In a table both statements of each version have the same truth value, thus making them equivalent statemnets. Thus the statement has the same value as its negated version. In negation the conjunction , change the conjunction to a disjunction : (p q) p q. In negating the disjunction , change the disjunction to a conjunction : (p q) p q. An argument is valid if the conclusion is true whenever the premises are assumed to be true.
