Does absolute value n+m= absolute value n + absolute value m for all integers n and m? If so give examples if not give a counterexample.

Answer 1

Only true for m ≥ 0, so in general the statement is false.

A counterexample for it being true ...
let n = 10, m = -5

Left side
= | 10 - 5| = 5
right side
= |10 + |-5| |
= |10+5|
= 15

LS ≠ Rs