Consider the statement S:"0×0=81 OR 1×1=81 OR 2×2=81 OR 3×3=81, and so on”. S is strictly a logical disjunction
Although individual statements are connected by ORs, the "and so on” makes it impossible to integrate and treat the statement strictly as a logical disjunction. The statement can also be written as
S: "For some non-negative integer n, n×n=81”
This phrase "for some non-negative integer” is special. It sums up infinite number of ORs.
The statement is true in our given case if n×n=81 for any of the n. A single solution is enough to prove that the existential quantifier is true.
In order to prove it wrong it is necessary to prove that there are absolutely no solutions.