Let x ∈ A ∩ B. Then x ∈ A and x ∈ B. Therefore, x ∈ A.
Here is a practical guide to finding exercises and solutions for Kunen’s Set Theory .
Show that if $M$ is a countable transitive model of ZFC and $\mathbbP \in M$ is a partial order, then there exists a $G \subseteq \mathbbP$ which is $M$-generic.
After finding a community solution, write it in your own words. Then modify the problem: e.g., “What if I replace $\omega_1$ with a singular cardinal?” This transforms the exercise into research.