Alright, I know how to show an annihilator is an ideal. I have a been working on these next problems for a bit, trying to see if I'm close

1. If $\displaystyle X\subseteq Y$, show that $\displaystyle ann(Y)\subseteq ann(X)$

2. Show that $\displaystyle ann(X\cup Y)=ann(X)\cap ann(Y)$

Thanks for any input guys.