Quantifiers

There are two types of quantifiers:

• $\forall$ (universal) - asserts that a property holds for all values of a variable in a given domain
• $\exists$ (existential) - asserts that a property holds for some values of a variable in a given domain

variables can are bound through Quantifiers. if a quantifier does not bind any variables it can be removed, quantifiers can only bind in its scope

when nesting quantifiers the order matters.

Universe of discourse

sometimes also know as the domain of discourse if we have a proposition: $\forall x.P(x)$ the variable $x$ is quantified by $\forall$, which means “for all $x$ in the universe of discourse.” The universe of discourse can represent any domain, such as:

• all people
• all animals
• Number_sets and or sets