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Truth Tables For p and q 

There are only 16 possible combinations of true and false for the two statements p and q. The tables below display those 16 combinations and common statements that produce them. See Symbols Used for an explanation of the coding.

    Tautology Disjunction &
Unless		 Converse &
Inverse		  
p q p -> p
p v (p ->q)		 p v q
~q -> p		 q -> p
~p -> ~q		 p
T T T T T T
T F T T T T
F T T T F F
F F T F T F

 

    Conditional &
Contrapositive		   Biconditional Conjunction &
Because
p q p -> q
~q -> ~p		 q p <-> q p ^ q
(p^q)^(q->p)
T T T T T T
T F F F F F
F T T T F F
F F T F T F

 

    No p is q Exclusive OR Not q  
p q p -> ~q
~(p ^ q)		 p |v| q ~q p ^ ~q
T T F F F F
T F T T T T
F T T T F F
F F T F T F

 

        Neither p nor q Self-
defeating
p q ~p ~(q -> p) ~(p v q) p ^ ~p
T T F F F F
T F F F F F
F T T T F F
F F T F T F

 

 

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Updated: December 10, 2003 00:50 -0500
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