Stating Truth-Tree Rules for non-PL Operators - Answers!

Here are three non-PL operators and their truth table definitions. For each one, state the truth-tree rule for it, and for the corresponding negation.

1.
p q (p % q)
T T F
T F F
F T F
F F T
(p % q)

~p

~q

 

 ~(p % q)

/           \

p             q

 

 

 

2.
p q (p ! q)
T T F
T F T
F T T
F F F
(p ! q)

/         \
p        ~p
~q        q

 

 ~(p ! q)

/             \
p             ~p
q             ~q

 

 

3.
p q (p ^ q)
T T F
T F F
F T T
F F T
(p ^ q)
/        \
~p     ~p    
q       ~q

 

 ~(p ^ q)

/             \
p           p
q           ~q

 

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