Work out truth table instantly with clear inputs, formula shown and shareable results.
A truth table lists every combination of input truth values and the resulting output. With two variables there are four rows; a formula true in all of them is a tautology and one true in none is a contradiction.
Implication
P → Q is false only when P is true and Q is false
Biconditional
P ↔ Q is true exactly when P and Q agree
An implication only promises something when the antecedent holds. With a false antecedent the promise is never tested, so it counts as kept.
2ⁿ. Three variables need 8 rows, four need 16.