The

universal quantifier, also known as "

for all." The

proposition ∀

*x* *P*(

*x*) translates into

English as "for all

*x* *P*(

*x*)" or "for every

*x* *P*(

*x*)".

It means that *P*(*x*) is true for all values of *x* in the universe of discourse (the domain under consideration). Used extensively in logic.