# Category:Existential Quantifier

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This category contains results about **Existential Quantifier**.

The symbol $\exists$ is called the **existential quantifier**.

It expresses the fact that, in a particular universe of discourse, there exists (at least one) object having a particular property.

That is:

- $\exists x:$

means:

**There exists at least one object $x$ such that ...**

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

- $\exists x \in S: \map P x := \set {x \in S: \map P x} \ne \O$

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

## Pages in category "Existential Quantifier"

The following 10 pages are in this category, out of 10 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