# Category:Biconditional

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This category contains results about **the biconditional operator**.

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

The **biconditional** is a binary connective:

- $p \iff q$

defined as:

- $\paren {p \implies q} \land \paren {q \implies p}$

That is:

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

## Subcategories

This category has the following 20 subcategories, out of 20 total.

### B

- Biconditional Elimination (9 P)
- Biconditional Introduction (6 P)
- Biconditional is Associative (2 P)
- Biconditional is Commutative (5 P)
- Biconditional is Reflexive (3 P)
- Biconditional is Transitive (4 P)
- Biconditional with Tautology (3 P)

### E

- Examples of Biconditional (2 P)

### N

### R

- Rule of Material Equivalence (7 P)

## Pages in category "Biconditional"

The following 33 pages are in this category, out of 33 total.

### B

- Biconditional as Disjunction of Conjunctions
- Biconditional Elimination
- Biconditional Equivalent to Biconditional of Negations
- Biconditional iff Disjunction implies Conjunction
- Biconditional in terms of NAND
- Biconditional Introduction
- Biconditional is Associative
- Biconditional is Commutative
- Biconditional is Reflexive
- Biconditional is Self-Inverse
- Biconditional is Transitive
- Biconditional of Proposition and its Negation
- Biconditional Properties
- Biconditional with Contradiction
- Biconditional with Factor of Biconditional
- Biconditional with Itself
- Biconditional with Tautology
- Binary Logical Connectives with Inverse

### C

### N

- 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
- Non-Equivalence of Proposition and Negation/Formulation 2