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.