Let two fair six-faced dice A and B be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die B shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

Question

$\begin{array}{1 1}(1)E_1 \;and\; E_2\; are\;independent \\ (2)E_2\; and\; E_3\; are\; independent \\ (3) E_1\; and\; E_3 are\; independent \\ (4) E_1, E_2 \;and \;E_3\; are\; independent \end{array}$