Could someone please check my work?

U16 = 21in2 Ler A and B be subsets of a universal set U = 21, 2, 3,43 ASB Prove That ALB = (UVB) ) (UVA ) 2 XEW and x's Suppose AIB & (UIEs,(UIA). 13 14 If XE AB, Then by The definition of complement XCA and x 4B. By The definition of subser XE (UJB); CUJA). By The definition of complement, UVA = [1,43 * E ( U( B) and * * (ULA) . (2 XEU and x to This means, XEW and XEB and if is not The Case That X EU and * EA, which Means either XEV or XEA. Since X GU, 4 XEA and we Then it Must be the case That XEA, since at least one or-clause Must be tree for the disjunction to be Tre. Hence, by The subset rule, AJB S ( UJB) ) (VIA). Now suppose ( USB ) ) (U) A) C A) B. If yE ( UJB)) (UV A), Then by definition of complement, YE cule) and y E (UIA). This means YEU and yeb and it is not The case That yEU and yKA, which means yEU or yeA. Since yEU, Then it MUST be the case That YEA. Since yEA and yEB, it follows by the definition of complement that yeAlB. Hence, by the it subser rude, ( UIB)) (Up A) S ALB. Therefore, 1 A\\B = (UJB) ) (UJA )