Truth Tables for the Not, Conjunction, Disjunction, Exclusive Or, and Conditional Operators

NOT
p p'
1 0
0 1

 



Not: a unary operator, such that when p is true, not p is false.

 

AND
p q p · q
1 1 1
1 0 0
0 1 0
0 0 0

 





Conjunction: p  AND q is true only when both p and q are true.

 

OR
p q p + q
1 1 1
1 0 1
0 1 1
0 0 0

 





Disjunction: p OR q is false only when both p and q are false.

 

XOR
p q p Å q
1 1 0
1 0 1
0 1 1
0 0 0

 

 

 

Exclusive Or: p XOR q is true only when either p or q is true, but not when both are true.

 

Conditional
p q p ® q
1 1 1
1 0 0
0 1 1
0 0 1



 by alternate representation




Conditional: If p then q if false only when the hypothesis is true and the conclusion is false. Note that when the hypothesis is false the conditional is vacuously true.

Order of precedence:

  1. Not
  2. Conjunction (AND), Disjunction (OR), Exclusive Or (XOR)
  3. Conditional (if-then)