Proving Set Equality: How to Show Subset Relationships?

[Sara jj]

1) $\cap_{i=1}^{n} A_{i}= A_{1}\setminus \cup_{i=1}^{n}(A_{1}\setminus A_{i})$

2) $\cap_{i=1}^{\infty} A_{i}= A_{1}\setminus \cup_{i=1}^{\infty}(A_{1}\setminus A_{i})$

 

[cbarker1]

You need to show that there are subsets to each other.

For example:
Let $A$ and $B$ be sets. Prove that $A=B$, ( to do that you need to show that $A \subseteq B$ and $B\subseteq A$ is true).