The following exercises cover the use of truth tables to check whether a formula is a tautology, whether two formulas are logically equivalent, and whether an argument is valid.
1. Simple truth tables
Populate the truth table for each formula. Sentence-letter columns are pre-filled.
Click each ? cell to cycle through T and F, then click Check to verify your answers.
A formula is a tautology if and only if it is true under every assignment of truth values.
Use the Build card to construct the truth table. Then click Evaluate
in the Check card to determine whether it is a tautology.
If it is not, a counterexample row will be highlighted in red.
Two formulas are logically equivalent if they have the same truth value on every row.
Use the Build card to construct the truth table for each formula. Then click
Evaluate in the Check card. Rows where the truth values differ will be highlighted.
An argument is valid if there is no assignment making all premises true and the conclusion false.
Premises are listed first; the conclusion is the last formula.
Click Evaluate in the Check card. Counterexample rows will be highlighted in red.