Truth tables

Lessons

• Introduction
  Truth Tables Overview:
  a)

  Negation Truth Tables
  
  
  b)

  Conjunction Truth Tables
  
  
  c)

  Disjunction Truth Tables
  
  
  d)

  Truth Tables with three or more statements
  
  

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• 1.
  Truth Tables with Negations, Conjunctions, and Disjunctions (two statements)

  Fill in the truth tables:

  a)

  $p$	$q$	~$p$	~$p$ ˅ $q$
  T	T
  T	F
  F	T
  F	F

  
  
  b)

  $p$	$q$	~$q$	$p$ ˄ ~$q$
  T	T
  T	F
  F	T
  F	F

  
  
  c)

  $p$	$q$	~$p$	~$q$	~$p$ ˄ ~$q$
  T	T
  T	F
  F	T
  F	F

  
  

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• 2.
  Construct a truth table for the following:
  a)

  $p$ ˅ ~$q$
  
  
  b)

  ~$p$ ˄ $q$
  
  

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• 3.
  Truth Tables with Negations, Conjunctions, and Disjunctions (three statements)

  Fill in the truth tables:

  a)

  $p$	$q$	$r$	~$p$	~$p$ ˅ $q$	(~$p$ ˅ $q$) ˄ $r$
  T	T	T
  T	T	F
  T	F	T
  F	T	T
  T	F	F
  F	F	T
  F	T	F
  F	F	F

  
  
  b)

  $p$	$q$	$r$	~$p$	~$q$	~$p$ ˄ ~$q$	(~$p$ ˄ ~$q$) ˅ $r$
  T	T	T
  T	T	F
  T	F	T
  F	T	T
  T	F	F
  F	F	T
  F	T	F
  F	F	F

  
  
  c)

  $p$	$q$	$r$	~$p$	~$r$	~$p$ ˅ ~$r$	(~$p$ ˅ ~$r$) ˄ $q$
  T	T	T
  T	T	F
  T	F	T
  F	T	T
  T	F	F
  F	F	T
  F	T	F
  F	F	F

  
  

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• 4.
  Construct a truth table for the following:
  a)

  $p$ ˅ $q$ ˅ $r$
  
  
  b)

  $p$ ˄ $q$ ˄ $r$
  
  

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