Bound Quantifier

Bound Quantifiers

This is when the Universe of Discourse is bounded $\forall x\in A,P(x)$ is short for $\forall x,x\in A⟹P(x)$ $\exists x\in A,P(x)$ is short for $\exists x,x\in A\wedge P(x)$

Bound Quantifiers When $A=\varnothing$

If $A$ is the empty set $\varnothing$ then, $\forall x\in \varnothing ,P(x)$ is Vacuously True $\exists x\in \varnothing ,P(x)$ is False

Quantifier Abbreviation

$\forall x(x\in A\to P(x))\equiv \forall x\in AP(x)$