# Category:Implication

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This category contains results about Implication in the context of Propositional Logic.

Definitions specific to this category can be found in Definitions/Implication.

The **conditional** or **implication** is a binary connective:

- $p \implies q$

defined as:

*If*$p$ is true,*then*$q$ is true.

This is known as a **conditional statement**.

A **conditional statement** is also known as a **conditional proposition** or just a **conditional**.

$p \implies q$ is voiced:

**if $p$ then $q$**

or:

**$p$ implies $q$**

## Subcategories

This category has the following 45 subcategories, out of 45 total.

### B

- Biconditional Elimination (9 P)

### C

- Clavius's Law (10 P)
- Constructive Dilemma (6 P)
- Contradictory Antecedent (3 P)
- Contradictory Consequent (3 P)

### D

- Destructive Dilemma (5 P)

### E

- Examples of Formal Implication (empty)

### F

- Factor Principles (23 P)

### H

### I

- Implication in terms of NAND (3 P)

### L

- Law of Excluded Middle (139 P)
- Law of Identity (14 P)

### M

- Modus Ponendo Ponens (19 P)
- Modus Ponendo Tollens (14 P)
- Modus Tollendo Ponens (21 P)

### P

- Peirce's Law (13 P)
- Praeclarum Theorema (6 P)
- Principle of Commutation (14 P)
- Principle of Composition (4 P)
- Principle of Dilemma (12 P)
- Proof by Cases (21 P)
- Proof by Contradiction (14 P)

### R

- Rule of Exportation (12 P)
- Rule of Implication (9 P)
- Rule of Material Equivalence (7 P)
- Rule of Material Implication (14 P)
- Rule of Transposition (40 P)

### S

### T

- Tautological Antecedent (3 P)
- Tautological Consequent (3 P)

## Pages in category "Implication"

The following 61 pages are in this category, out of 61 total.

### C

- Clavius's Law
- Conditional and Converse are not Equivalent
- Conditional and Inverse are not Equivalent
- Conditional iff Biconditional of Antecedent with Conjunction
- Conditional iff Biconditional of Consequent with Disjunction
- Conditional is not Associative
- Conditional is not Commutative
- Conditional is not Right Self-Distributive
- Conditional/Semantics of Conditional/Examples
- Conjunction and Implication
- Conjunction Equivalent to Negation of Implication of Negative
- Conjunction with Negative Equivalent to Negation of Implication
- Constructive Dilemma
- Contradictory Antecedent
- Contradictory Consequent
- Converse of Conditional is Contrapositive of Inverse
- Converse of Conditional is Inverse of Contrapositive