1. ## Proving sets equality

A and B are sets,
Prove that if 𝐴∖𝐵=∅ and 𝐵∖𝐴=∅ then 𝐴=𝐵 .

Now i know it has something to do saying that X is in set A or something like that but im kinda stuck.
Any help? need the general idea

also have a thing where i dont know how to actually write the solution in this :

A,B,C are sets,
prove that if 𝐴∩𝐶⊆𝐵∩𝐶 and 𝐴∩𝐶̅'⊆𝐵∩𝐶' then 𝐴⊆𝐵 (using ' for NOT)

I know that 𝐴∩𝐶 and 𝐴∩𝐶̅' will give me everything in A, and the same for the other side will give me B but i dont know how to write it in an actual solution form.

2. ## Re: Proving sets equality

Originally Posted by Wesix
A and B are sets,
Prove that if 𝐴∖𝐵=∅ and 𝐵∖𝐴=∅ then 𝐴=𝐵 .
\displaystyle \begin{align*}A\setminus B&=A\cap B^c=\emptyset \\B\setminus A&=B\cap A^c=\emptyset\\ [A\cap B^c=\emptyset] & \Rightarrow A\subseteq B\\ [B\cap A^c=\emptyset] & \Rightarrow B\subseteq A\end{align*}

Can you finish?

3. ## Re: Proving sets equality

Originally Posted by Plato
\displaystyle \begin{align*}A\setminus B&=A\cap B^c=\emptyset \\B\setminus A&=B\cap A^c=\emptyset\\ [A\cap B^c=\emptyset] & \Rightarrow A\subseteq B\\ [B\cap A^c=\emptyset] & \Rightarrow B\subseteq A\end{align*}

Can you finish?
Yes that helped, Ty.