Made Easy Test Series:Discrete Math-Mathematical Logic

Question

Consider the following first order logic statement

$I)\forall x\forall yP\left ( x,y \right )$

$II)\forall x\exists yP\left ( x,y \right )$

$III)\exists x\exists yP\left ( x,y \right )$

$III)\exists x\forall yP\left ( x,y \right )$

Which one of the following is not true about $I,II,III,IV?$

$A)$ If $II)$ is true , then $III),IV)$ is true

$B)$  If $IV)$ is true , then $II),III)$ is true

$C)$ None of these

Answer 1

is option b is correct???