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associative law

Regrouping a chain of "and"s, or a chain of "or"s, doesn't change its truth value.

The associative laws state that (A ∧ B) ∧ C ≡ A ∧ (B ∧ C) and (A ∨ B) ∨ C ≡ A ∨ (B ∨ C). They do not hold when the connectives are mixed or for the conditional.

Examples

  • (P ∨ Q) ∨ R and P ∨ (Q ∨ R) have the same truth table.

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