Consider a proper binary search tree in Java with $N$ nodes, $H$ height, E external nodes, and I internal nodes. Which of the following options is correct?

$1E{2}^H$

$HI{2}^H-1$

$\frac{log(N+1)-1}{2}H\frac{N-1}{2}$

$1E{2}^H$

$HI{2}^H-1$

$log(N+1)-1HN-1$

$1E{2}^{\text{'}\text{'}}$

$HI{2}^H-1$

$log(N+1)-1H\frac{N-1}{2}$