# Category:Logical Negation

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This category contains results about **the negation operator of propositional logic**.

Definitions specific to this category can be found in Definitions/Logical Negation.

The **logical not** or **negation** operator is a unary connective whose action is to reverse the truth value of the statement on which it operates.

- $\neg p$ is defined as:
**$p$ is not true****It is not the case that $p$ is true****It is false that $p$****$p$ is false**.

Thus the statement $\neg p$ is called the **negation** of $p$.

$\neg p$ is voiced **not $p$**.

## Subcategories

This category has the following 24 subcategories, out of 24 total.

### C

### D

- De Morgan's Laws (Logic) (50 P)
- Destructive Dilemma (6 P)

### E

- Examples of Logical Negation (2 P)

### M

- Modus Ponendo Tollens (13 P)
- Modus Tollendo Ponens (20 P)

### N

### P

- Principle of Dilemma (13 P)
- Proof by Contradiction (15 P)

### R

- Rule of Material Implication (16 P)
- Rule of Transposition (40 P)

## Pages in category "Logical Negation"

The following 30 pages are in this category, out of 30 total.

### C

### D

### N

- Negation implies Negation of Conjunction
- Negation of Conditional implies Antecedent
- Negation of Conditional implies Negation of Consequent
- Non-Equivalence
- Non-Equivalence as Conjunction of Disjunction with Disjunction of Negations
- Non-Equivalence as Conjunction of Disjunction with Negation of Conjunction
- Non-Equivalence as Disjunction of Conjunctions
- Non-Equivalence as Disjunction of Negated Implications
- Non-Equivalence as Equivalence with Negation