I am having a hard time showing this simple relation. Here, all the letters below are in $\mathbb{N} \cup \{0\}$. $A = \{(a,b) : a + 2b \leq n+2\}$ $B = \{(a,c+1) : a + 2c \leq n\}$
How to show that $B \subset A$?
This is something I got from a sum over the above indices. I wanted a lower bound on the sum (which is where $B$ came in). Obviously I set $b = c+1$ in $A$ to get $B$ but how to show that it's a subset?
Thanks