Question

Let P(x) denote 'x is a person' and Q(x) denote 'x drinks coffee'.
Consider the statement.
"Some persons do not drink coffee".
Which of the following first order logic sentence correctly represents the negation of the above statement ?

• A. $\forall x${P (x) $\to$ Q(x)}
• B. $\exists x${P (x) $\to$ ~Q(x)}
• C. $\exists x${P (x) $\wedge$ ~Q(x)}
• D. $\forall x${P (x) $\wedge$ Q(x)}

Answer 1

The correct option is A $\forall x${P (x) $\to$ Q(x)}

The given statement can be expressed as
$\exists x${P (x) $\wedge$ ~Q(x)}
It's negation is
$\forall x${P (x) $\to$ Q(x)}