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