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

**Takeaway Points**

- 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.
- 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:

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