I am stuck on a proof:
Let $x$ and $y$ be any two vectors in $F_q.$ Show that $wt(x+y)>= |wt(y) - wt(x)|$, where wt(.) denotes the hamming weight.
Now I know that $wt(x+y)$ is the cardinality of all non-zero indices of x+y,
I need help in showing mathematically how $wt(x+y) >= |wt(y) - wt(x)|$
If anyone could suggest that would be great! thank you