Logical Negation: Understanding "Not O"

In logic, the negation of a proposition o is "not o" (symbolically ¬o, ~o, or o′). It reverses the truth value: if o is true, ¬o is false, and vice versa.

Examples

• o = "It is sunny outside." → ¬o = "It is not sunny outside."
• o = "The door is open." → ¬o = "The door is not open." (i.e., closed)
• o = "x > 5" → ¬o = "x ≤ 5"

Truth Table

o	¬o
True	False
False	True

Related Concepts

• De Morgan's Laws: ¬(A ∧ B) ≡ ¬A ∨ ¬B; ¬(A ∨ B) ≡ ¬A ∧ ¬B
• Double negation: ¬(¬o) ≡ o
• Contradiction: o ∧ ¬o is always false.

Negation is fundamental in propositional logic, programming, mathematics, and formal reasoning.