If $0 \leq a_n \leq b_n$ for all $n$ and $\sum b_n$ converges, then $\sum a_n$ converges

If $0 \leq a_n \leq b_n$ for all $n$ and $\sum a_n$ diverges, then $\sum b_n$ diverges

If $0 \leq b_n \leq a_n$ for all $n$ and $\sum a_n$ converges, then $\sum b_n$ converges

If $0 \leq a_n \leq b_n$ for all $n$ and $\sum b_n$ diverges, then $\sum a_n$ diverges