Mistakes give rise to Problems- 4

Algebra Level 5

If you distribute the \(\textbf{modulus}\) sign over the content in it, it's a mistake, i.e. \[\left| a+b \right| = \left| a \right| + \left| b \right|\] This is a \(\color{Red}{\textbf{big mistake}}\), it's a \(\color{Blue}{\textbf{false property}}\)!

But for how many pairs of integers \((a,b)\) such that \(-10 \leq a \leq 10\) and \(-10 \leq b \leq 10\), is the above said "false" property seen to be "true" ?