# Category:Universal Quantifier

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This category contains results about **the universal quantifier**.

Definitions specific to this category can be found in Definitions/Universal Quantifier.

The symbol $\forall$ is called the **universal quantifier**.

It expresses the fact that, in a particular universe of discourse, all objects have a particular property.

That is:

- $\forall x:$

means:

**For all objects $x$, it is true that ...**

In the language of set theory, this can be formally defined:

- $\forall x \in S: \map P x := \set {x \in S: \map P x} = S$

where $S$ is some set and $\map P x$ is a propositional function on $S$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Universal Quantifier"

The following 14 pages are in this category, out of 14 total.

### D

- De Morgan's Laws (Predicate Logic)
- De Morgan's Laws (Predicate Logic)/Assertion of Existence
- De Morgan's Laws (Predicate Logic)/Assertion of Universality
- De Morgan's Laws (Predicate Logic)/Denial of Existence
- De Morgan's Laws (Predicate Logic)/Denial of Universality
- De Morgan's Laws (Predicate Logic)/Denial of Universality/Formulation 1
- De Morgan's Laws (Predicate Logic)/Denial of Universality/Formulation 2
- De Morgan's Laws (Predicate Logic)/Denial of Universality/Formulation 2/Forward Implication
- De Morgan's Laws (Predicate Logic)/Denial of Universality/Formulation 2/Reverse Implication