Q33

MCQ2 marks, −0.5

Consider the following formula and its two interpretations $I_1$ and $I_2$ . $\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]$ $I_1$ : Domain: the set of natural numbers $P_x$ = ' $x$ is a prime number' $Q_{xy}$ = ' $y$ divides $x$ ' $I_2$ : same as $I_1$ except that $P_x$ = ' $x$ is a composite number'. Which of the following statements is true?

(A)

$I_1$ satisfies $\alpha$ , $I_2$ does not

(B)

$I_2$ satisfies $\alpha$ , $I_1$ does not

(C)

Neither $I_1$ nor $I_2$ satisfies $\alpha$

(D)

Both $I_1$ and $I_2$ satisfies $\alpha$

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