A universal existential statement is a statement that is universal because its first part says that a certain property is true for all objects of a given type, and it is existential because its second part asserts the existence of something.
For example:
Every real number has an additive inverse.
Brielfy a mathematical statement is a sentence which is either true or false. For example ``The square root of 4 is 5" is a mathematical statement (which is, of course, false). ... In mathematics we use language in a very precise way, and sometimes it is slightly different from every day use.
An existential statement is a statement that is true if there is at least one variable within the variable's domain for which the statement is true.
