Question

Find the argument form for the following argument and determine whether it is valid. Can we conclude that the conclusion is true if the premises are true?
If George does not have eight legs, then he is not a

spider. George is a spider. George has eight legs.

Short answer

The argument form can be found and valid can be determined.

Step-by-step solution

Construct the truth table for the premises

The argument is in Modus Tollens form. The symbol ‘~’ denotes the converse of the concerned assumption. The construction of truth table for the premises as,

p	q	\(p \to q\)	~q	~p (conclusion)
T	T	T	F	F
T	F	F	T	F
F	T	T	F	T
F	F	T	T	T

Conclusion for the premises

There is an assumption in premises of \(p \to q\)is true and q is false. There is only 1 line in truth table and satisfies these two conditions. ~p is true and ~q is true i.e., p is false. It is concluded that premises are true and ~p is also true or p is false.