Question

Consider the statement $S:"0\times 0=81\text{OR}1\times 1=81\text{OR}2\times 2=81\text{OR}3\times 3=81$, and so on”. S is strictly a logical disjunction

• A. True
• B. False

Answer 1

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 $n,n\times n=81$”

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 $n\times n=81$ 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.