Truth Tables
Objectives:
  • Construct a truth table for a given symbolic expression.
  • Determine if two given statements are equivalent using truth tables.
  • Use De Morgan’s Laws to write a statement equivalent to a given statement.


Vocabulary:
  • truth table
  • equivalent expressions
  • De Morgan’s Laws
Negation
p
 ~p
T
F

Conjunction
p
 q
 p and q
T
 T
T
 F
F
 T
F
 F

Disjunction
p
 q
 p or q
T
 T
T
 F
F
 T
F
 F

Conditional
p
 q
 p implies q
T
 T
T
 F
F
 T
F
 F

Click here for a video explaining how to fill in the truth tables.

Possible Classroom Examples:
p
 ~p
 p or not p







p q
 p and q
 ~q
 p and q implies not q





















If the lyrics are not controversial, then performance is not banned.
p:
q:
symbolic form:
p
 q  
 
      





















The country singer is in trouble if he is elected.
p:
q:
symbolic form:
p
 q  
 
      





















If he does not go to jail, he is innocent or has an alibi.
p:
q:
r:
symbolic form:
p
 q r
  





      

























































































p
 q
   
  
  





















p
 q
   
  
  





















The streets are wet or it is not raining.

If it is raining, then the streets are wet.
p:
q:

symbolic form:
symbolic form:
p
 q
  
 
 






















p
 q
  
 
 






















© 2007 Elizabeth E. K. Jones and the ASU Department of Mathematics and Statistics - All rights reserved.