Question

can someone explain too me what happen at this last step of this proof?

Answer 1

ok i got it

Answer 2

You'd do this by set inclusion. If we can show that 𝐴−(𝐴∩𝐵)⊂𝐴−𝐵, and that 𝐴−𝐵⊂𝐴−(𝐴∩𝐵)

, we'd conclude equality.

So let 𝑥∈𝐴−𝐵
. Then 𝑥∈𝐴,𝑥∉𝐵, so 𝑥∉𝐴∩𝐵, and so 𝑥∈𝐴−(𝐴∩𝐵)

.

If 𝑥∈𝐴−(𝐴∩𝐵)
, 𝑥∈𝐴 but not in 𝐴∩𝐵. If 𝑥∈𝐵 we'd have a contradiction. That finishes the proof.