Symbol indicating that a property is applied to all of the elements in a set or only to some of them.

### Symbols

- The
**universal quantifier**is “\(\forall\)*x*∈ E ” which is read as: “for any*x*element of set E” or “given any*x*element of set E”. - The
**existential quantifier**is “\(\exists\)*x*∈ E” which is read as: “there is at least one*x*element of set E”. - The
**uniqueness quantifier**is \(\underset{1}{\exists}\) which is read as: “there is one and only one*x*element of set E”.

### Examples

- The expression “\(\forall\)
*x*∈ \(\mathbb{N}\) : (*x*+ 4) ∈ \(\mathbb{N}\)” is read as: “given any whole number*x*, (*x*+ 4) is a whole number”. - The expression “\(\exists\)
*x*∈ \(\mathbb{N}\) :*x*is a divisor of 12″ is read as: “there is at least one whole number*x*for which*x*is a divisor of 12″. - The expression “\(\forall a, b ∈ \mathbb{R},\space \textrm{with }b ≠ 0, \underset{1}{\exists}x ∈ \mathbb{R} : \dfrac{a}{b} = x\), is read as “for all numbers
*a*and*b*of the set of real numbers,*b*being zero, there is one and only one*x*element of the set of real numbers for which the quotient of*a*by*b*is equal to*x*“.