Definition:Universal Quantifier

The symbol $$\forall$$ means "for all ...". This is called the universal quantifier.

$$\forall x:$$ means: "For all objects $$x$$, it is true that ...".

Some authors use $$\left({x}\right)$$ to mean $$\forall x$$, but the bespoke symbol is usually preferred as there is then no room for ambiguity.

A universal statement is one which expresses the fact that all objects (in a particular universe of discourse) have a particular property.