# Definition:Conditional/Language of Conditional

## Contents

## Definition

The conditional has been discussed at great length throughout the ages, and a whole language has evolved around it. For now, here are a few definitions:

### Weak

In a conditional $p \implies q$, the statement $q$ is **weaker** than $p$.

### Strong

In a conditional $p \implies q$, the statement $p$ is **stronger** than $q$.

Thus we have the notion of certain theorems having a weak and a strong version.

### Superimplicant

In a conditional $p \implies q$, the statement $p$ is **superimplicant** to $q$.

### Subimplicant

In a conditional $p \implies q$, the statement $q$ is **subimplicant** to $p$.

### Antecedent

In a conditional $p \implies q$, the statement $p$ is the **antecedent**.

### Consequent

In a conditional $p \implies q$, the statement $q$ is the **consequent**.

### Necessary Condition

Let $p \implies q$ be a conditional statement.

Then $q$ is a **necessary condition** for $p$.

That is, if $p \implies q$, then it is *necessary* that $q$ be true for $p$ to be true.

This is because unless $q$ is true, $p$ can *not* be true.

### Sufficient Condition

Let $p \implies q$ be a conditional statement.

Then $p$ is a **sufficient condition** for $q$.

That is, if $p \implies q$, then for $q$ to be true, it is *sufficient* to know that $p$ is true.

This is because of the fact that if you know that $p$ is true, you know enough to know also that $q$ is true.