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 Socrates is human, then Socrates is mortal. Socrates is human. Socrates is mortal.

Short answer

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

Step-by-step solution

Constructing the truth table for the premises

Take p be the proposition for “Socrates in human” and q be “Socrates is mortal”. There is an abstract form in the argument. The argument is in Modus ponens form. The construction of truth table for the premises as,

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

Conclusion for the premises

The first row is the only row when there are two true premises and conclusion also true. So that the Modus Ponens is valid. It will use a conditional statement when p and q are true. The second assumption is true p statement. It concluded that when there are true premises then conclusion also true.