Explain the error of a sum or a difference.

(N/A) Let two physical quantities $A$ and $B$ have measured values $A \pm \Delta A$ and $B \pm \Delta B$,respectively.
$(i)$ For addition:
Let $Z$ be the quantity obtained by the addition of $A$ and $B$.
$Z = A + B$
Let the error in $Z$ be $\Delta Z$.
$Z \pm \Delta Z = (A \pm \Delta A) + (B \pm \Delta B)$
$Z \pm \Delta Z = (A + B) \pm (\Delta A + \Delta B)$
Since $Z = A + B$,we have $\pm \Delta Z = \pm \Delta A \pm \Delta B$.
For the maximum absolute error,$\Delta Z = \Delta A + \Delta B$.
$(ii)$ For subtraction:
Let the difference of $A$ and $B$ be $Z$.
$Z = A - B$ (where $A > B$)
$Z \pm \Delta Z = (A \pm \Delta A) - (B \pm \Delta B)$
$Z \pm \Delta Z = (A - B) \pm \Delta A \mp \Delta B$
Since $Z = A - B$,we have $\pm \Delta Z = \pm \Delta A \mp \Delta B$.
The possible values for $\Delta Z$ are $\Delta A - \Delta B$ or $-\Delta A + \Delta B$ or $\Delta A + \Delta B$ or $-\Delta A - \Delta B$.
For the maximum absolute error,$\Delta Z = \Delta A + \Delta B$.