$\underline{\mathbf{Answer:C}}$
$\underline{\mathbf{Explanation:}}$
For calculating $\color{green}{{\textbf{predecessor}}}$ and the $\color{green}{\textbf{successor}}$ we need to get the $\underline{\color{magenta}{\textbf{"inorder traversal"}}}$ of the binary tree.
$\color{magenta}{\underline{\textbf{Inorder traversal:}\Rightarrow}}$ $\color{blue}{\mathbf{DBHEM\color{red}{\bbox[orange, 3px, border:1px solid green]{I}}\color{black}{\enclose{circle}{\Large A}}\color{red}{\bbox[orange, 3px, border:1px solid green]{J}}FNKCLG}}$
In the result, which is obtained after getting inorder of the binary tree, the element which will come before the given node, $\mathbf{i.e.}\;\enclose{circle}{\mathbf {\color {magenta} I}}$ will be the predecessor and the element which will come afterwards will be the successor, $\mathbf{i.e.\;\enclose{circle} {\color {magenta} J}}$ will be the successor.
So, here $\color{red}{\mathbf{predecessor\; of\; A\; is\; \bbox[orange,5px, border:2px solid red]{\enclose{circle}{I}}}}$ and the $\color{green}{\mathbf{successor\;of\;A\; is\; \bbox[orange,5px, border:2px solid green]{\enclose{circle}{J}}}}$
$\therefore\mathbf C$ is the correct answer.