Counterexample method
Tautology check with a counterexample
How to enter formulas
| Operation | How to enter |
|---|---|
| negation | ¬p ~p !p -p not p |
| conjunction | p ∧ q p & q p * q p ^ q p and q |
| disjunction | p ∨ q p | q p + q p or q |
| sum modulo 2 | p ⊕ q p xor q |
| implication | p → q p -> q p => q |
| equivalence | p ↔ q p <-> q p <=> q p ~ q p = q |
| constants | 0 1 |
Precedence from strongest to weakest: ¬, ∧, ∨, →, ⊕, ↔. For example, p → q ⊕ r reads as (p → q) ⊕ r, and p ∧ q ∨ r as (p ∧ q) ∨ r. Implication is right-associative: p → q → r = p → (q → r). Parentheses work as usual.