So here I have a question: $$\neg (B-A)=(\neg B) \cup_{}^{}(A\cap_{}^{}B)$$
Note that the negation symbol is actually used to represent the compliment symbol because I could not find a symbol for the compliment. I came up with a solution for this and wanted to verify it. Instead of proving this by showing that they are subsets of each other, I will use boolean algebra to show it is logically equivalent, by first converting the set operations to boolean operations and use DeMorgan's Law. Would this be valid? Or should I stick to proving that they are subsets of each other?