Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate

$P (x) =⇁ (x = 1) \land \forall y (\exists z (x = y * z))$

$\Rightarrow (y = x) \lor (y = 1)$

(P(x) being true means that x is a prime number

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P(x) being true means that x is a number other than 1

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P(x) is always true irrespective of the value of x

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P(x) being true means that x has exactly two factors other than 1 and x

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Solution

The correct option is A (P(x) being true means that x is a prime number
If P(x) is true, then

$x \neq 1$ and also

x is broken into two factors, only if, one of the factors is x itself and other factor is 1, which is exactly the definition of a prime number.

So P(x) is true means x is a prime number.

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