MinHeap represented by an array - two simple statements I'm trying to prove/disprove two statements. I just want to make sure with you I'm on the right line.

These are the following statements:

Preface : Let A[n] be an array of min-heap (a min-heap represented by an array], whereas all the elements in the heap are different from each other. 
Let i and j be two indexes in the range : $0 \le i, j \le n-1$.

Prove or disprove : 


If $i &lt; j $ then $A[i] &lt; A[j]$
If $A[i] &lt; A[j] $ then $i &lt; j$


I believe I managed to disprove both of them using the following heap:

$\qquad [2, 6, 7, 11, 14, 13, 12, 12, 13,15, 16, 71, 72, 13, 81]$

For:


Simply plug in the following indexes: $i = 4$ and $j = 13$. 

So $i &lt; j$ but $A[i] &gt; A[j]$.
Simply plug in the following indexes: $i = 13$ and $j = 4$.

So $A[i] &lt; A[j]$ but $i &gt; j$.


Am I missing something here? Or It is really that easy?
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).