Tutorial Problems 11 - For Week 12

1.    Use the method of truth trees for FDE to test whether the following arguments are valid in FDE. If any are not, construct counterexamples.

 

       a.    p & ~p; therefore q

       b.    p; therefore q v ~q

       c.    p, p É q; therefore q

 

2.    The method of truth trees for FDE can easily be adapted to other many-valued logics. Make the proper adaptations for the logic PŁ3.

       Note that here D = {1}, and you will need to add the following closing rule:

 

            A branch of the tree is closed if p Å and ~p Å both appear in that branch. (Why?)

 

3.    Use the method derived in 2 to test whether the following are tautologies/valid arguments in PŁ3. If any are not, construct counterexamples.

    

       a.    p É (q É p)

       b.    ~~p É p

       c.    p É q, q É r; therefore p É r