Question

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

A

True

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B

False

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Solution

The correct option is B False 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.

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