Logic Truth Table Generator
Generate a full propositional logic truth table for two variables P and Q, covering AND, OR, XOR, implication, and biconditional.
| P | Q | ¬P | P ∧ Q (AND) | P ∨ Q (OR) | P ⊕ Q (XOR) | P → Q | P ↔ Q |
|---|---|---|---|---|---|---|---|
| T | T | F | T | T | F | T | T |
| T | F | F | F | T | T | F | F |
| F | T | T | F | T | T | T | F |
| F | F | T | F | F | F | T | T |
Propositional Logic Truth Table Mathematics
Truth table generator produces a full propositional logic table for two variables P and Q, covering AND, OR, XOR, implication, and biconditional.
A truth table exhaustively lists every combination of true/false inputs and the resulting output for each logical operator — the definitive way to verify or discover a logical equivalence, like implication being equivalent to "not P or Q".
- 1The generator lists all four combinations of P and Q (true/true, true/false, false/true, false/false).
- 2For each row, it evaluates NOT P, AND, OR, XOR, implication (P→Q), and biconditional (P↔Q).
Find the truth value of the implication P → Q for the row where P is true and Q is false.
Frequently Asked Questions (FAQ)
Only in exactly one case: when P is true and Q is false. In every other combination — including when P is false — the implication is considered true.
OR (∨) is true if at least one input is true, including when both are true. XOR (⊕, "exclusive or") is true only when exactly one input is true — it excludes the both-true case that OR includes.
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