Truth Values and Truth Tables

A truth table lists every possible truth-value assignment for the simple propositions in a formula. If there are n distinct proposition letters, there are exactly 2ⁿ rows.

For two letters P and Q, the standard ordering is TT, TF, FT, FF. For three letters, P changes every four rows, Q every two rows, and R every row. This repeating-block pattern is more reliable than memorizing a finished table.

Evaluate from the inside out

Do not treat a long expression as one opaque operation. Identify its nested subexpressions, evaluate their children, and then apply the connective at each node. The final column can then be classified:

• tautology — final column is always true;
• contradiction — final column is always false;
• contingent — final column contains both truth values.

The Truth Table lab exposes the same structure used by the deterministic evaluator, so selecting a cell shows the operand values that produced it.