Verified answer

Moreso, the equation:

A - B = A ∪ B

is true exactly when B = ∅

Proof goes in two cases:

CASE 1 --- B = ∅

Then A - B = A - ∅ = A

And also A ∪ B = A ∪ ∅ = A

So A - B = A ∪ B if B = ∅

CASE 2 --- B is not empty.

Then consider some b in B.

b is not in A - B, since none of B is in A - B

But b must be in A ∪ B, since it's a union.

Thus A - B ≠ A ∪ B if B ≠ ∅.

what's that symbol on the right hand side? can you please clarify?