How to Construct a Truth Table

1. Make the first row of the table consisting of all the variables followed by a fully parenthesised version of the formula.
2. Write down n columns that encode the possible interpretations underneath the variables. This yields rows.
3. Systematically fill in the columns under the connectives
   • Start with connectives that apply only to atomic sentences.
   • Once this is done we work on sentences whose main connective has already had its value filled in.
   • Carry on until the the main connective of the sentence is filled in.

 
• Truth Table for a Complex Sentence