or

ask mattrab Visit www.askmattrab.com for more academic resources.

Truth Table

Hello Readers!!
Please go through 
this note before reading this!!




Truth Table for Logical Connectives
(where ' p ' and ' q ' are two statements)
1. Negation

p

q

~p

~q

T

T

F

F

T

F

F

T

F

T

T

F

F

F

T

T


2.Conjunction

p

q

p ᴧ q

T

T

T

T

F

F

F

T

F

F

F

F


3.Disjunction

p

q

v q

T

T

T

T

F

T

F

T

T

F

F

F


4.Conditional

p

q

 q

T

T

T

T

F

F

F

T

T

F

F

T


5. Biconditional 

p

q

 q

T

T

T

T

F

F

F

T

T

F

F

T



Tautology
        A compound statement which is always true, whatever may be the truth values of its components, is known as a tautology.
        EXAMPLE;

p

q

p v q

~p

(~p) ᴧ q

[(~p) ᴧ q] ⇒ (p v q)

T

T

T

F

F

T

T

F

T

F

F

T

F

T

T

T

T

T

F

F

F

T

F

T

 


Contradiction
        A compound statement which is always false, whatever may be the truth values of its components, is known as a tautology.
        EXAMPLE;

p

q

p v q

~(p v q)

~(p v q) ᴧ q

T

T

T

F

F

T

F

T

F

F

F

T

T

F

F

F

F

F

T

F

 


Laws of Logic [Important for Boolean Algebra (Computer)]
Law of Excluded middle :  Only one statement or 
~is true.
Law of Tautology             :  The disjunction of a statement and its negation is                                                           a tautology. 
Law of Contradiction      :  The conjunction of a statement and its negation is                                                         a contradiction. 
Law of Involution             :  The negation of negation of the statement is                                                                   logically equivalent to a given statement.

Law of Syllogism             :   If p→ q and q→ r then p→ r i.e.,
                                                       ( p →  q)  Λ (q→  r) →  (p →  r)  
Law of Contrapositive     :   ( p ⇒  q)   ≡   (∼ q ) ⇒  (∼ p )
                                                              The conditional and its contrapositive are                                                                     logically equivalent.
Law of Inverse                  :  (∼ p)  ⇒ (∼ q)  ≡ q ⇒p
                                                     The inverse and the converse of a conditional                                                              are logically equivalent.