Which one of the following options is CORRECT given three positive integers…

GATE · 2011 · CS · Computer Science & IT

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

P(x)=¬(x=1)∧∀y(∃z(x=y∗z)⇒(y=x)∨(y=1))P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left(\exists z\left(x=y*z\right) \Rightarrow \left(y=x\right) \vee \left(y=1\right) \right)

  1. A.

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

  2. B.

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

  3. C.

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

  4. D.

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

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