MinHeap represented by an array - two simple statements
You're not missing anything, this problem really is that easy. Your solution works, but I feel like I should point out that you can disprove both statements with a much smaller heap. In particular

\begin{array}{}
[2, 7, 6]
\end{array}

with $i = 1$ and $j = 2$ for the first statement and swapping them for the second.

Furthermore, I'm pretty sure those two statements only hold if the array is sorted (assuming distinct elements).