Check whether two logical statements are equivalent, with a full truth table. Every step is labeled with the rule it uses and rendered in proper math notation, so you can follow how the answer comes together. Type in your problem to start. Free to use, no account required.
Example
¬(p ∧ q) ≡ ¬p ∨ ¬q → equivalent — De Morgan's law
Tips
Separate the two formulas with ≡ (== and iff also work). Operators can be words or symbols: and/∧, or/∨, not/¬, -> for implication, <-> for biconditional, xor/⊕.
Two formulas are equivalent when their truth-table columns agree on every row. When they disagree, you get the counterexample: the exact assignment where the two sides differ.
Laws worth checking: De Morgan, the contrapositive (p → q ≡ ¬q → ¬p), the implication law (p → q ≡ ¬p ∨ q), and the distributive laws.