The existential quantifier
The existential quantification of P(x) is the proposition “there exists
an element x in the universe of discourse such that P(x) is true”.
It is written as ?xP(x) and read as
“there is an x such that P(x)”, or “for some x P(x)”.
Example. Let the universe of discourse be the set of positive integers.
What is the truth value of ?x(x+x=x?x) ?
What is the truth value of ?x(x=x+1) ?
If the universe of discourse is {a1,a2,…,an}, how can we express
?xP(x) without quantifiers?
---- P(a1) ? P(a2) ? … ? P(an)