Truth Tables

We now begin our unit on truth tables, which allow us to make logical deductions in an algorithmic manner.

Takeaway Points

  1. When are complex statements like ~(P ^ Q) ^ (R => Q) true? It is difficult to figure this out just by looking at it, and it would be even harder if we added a fourth simple sentence to the mix.
  2. Truth tables break those larger expressions down into smaller parts, allowing us to analyze each component individually and discover when the overall expression is true.

The algorithm for building a truth table is as follows:

  1. Create a column for each simple sentence.
  2. Create another column for each additional more complex expression in order of complexity.
  3. Fill in all possible truth value for all simple sentences.
  4. Going from left to right in the columns, use previous columns to deduce the truth value of current columns.

Back to Logic 101