# Category:Implication

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 43 subcategories, out of 43 total.

### B

### C

### D

### E

### F

### H

### I

### L

### M

### P

### R

### S

### T

## Pages in category "Implication"

The following 58 pages are in this category, out of 58 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 Left 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