If A, B, C are subsets of a set X and $$A^1 = X - A$$, then $$\left(A \cup \left(B^1 \cap C^1\right)\right) =$$

$$A^1 = X - A$$, then $$\left(A \cup \left(B^1 \cap C^1\right)\right) = $$

• Let S{x|x∈A−(B∩C)}S{x|x∈A−(B∩C)} Let Q{y|y∈(A−B)∪(A−C)}Q{y|y∈(A−B)∪(A−C)}
• All x∈Ax∈A and x∉B,Cx∉B,C.
• All y∈Ay∈A and y∉B,Cy∉B,C.
• Because all xx fit the definition of QQ then we say S⊆QS⊆Q
• Because all yy fit the definition of SS then we say Q⊆SQ⊆S
• Since S⊆QS⊆Q and Q⊆SQ⊆S then S=Q⟹A−(B∩C)=(A−B)∪(A−C)S=Q⟹A−(B∩C)=(A−B)∪(A−C) 

But then quickly realized it was wrong because the xx from set SS must meet the following criteria:

$$\left(A \cup \left(B^1 \cap C^1\right)\right) $$  Answer