Example 3

We can use this method to test the validity of arguments

If the argument A, B, therefore C is valid, i.e. A, B |= C then, if a model a model satisfies A and B it will also satisfy C. So the set A, B, ØC cannot be satisfied, and a tree constructed from that set will have no open branches

Consider the argument ("x)(Fx ® Gx), Fa, therefore Ga.

Contruct the tree:

   a  \      1.    Ø("x)(Fx ® Gx)           

              2.    Fa

              3.    ØGa

              4.    Fa ® Ga                         1, UI. Note: a has already occurred.

                          /     \                              

              5.    ØFa        Ga                    4              

              6.       X          X                    2, 5 and 3, 5

The tree closes. The argument is valid.