Let's verify the given statement: A ∪ (B ∩ C) = (A ∪ B) - (A ∪ C)
Step 1: Calculate (B ∩ C)
B ∩ C = {C, E, G, I} ∩ {O, A, E, H, I} = {A, E, I}
Step 2: Calculate A ∪ (B ∩ C)
A ∪ (B ∩ C) = {A, B, D, E, G} ∪ {A, E, I} = {A, B, D, E, G, I}
Step 3: Calculate (A ∪ B) and (A ∪ C)
(A ∪ B) = {A, B, D, E, G} ∪ {C, E, G, I} = {A, B, C, D, E, G, I}
(A ∪ C) = {A, B, D, E, G} ∪ {O, A, E, H, I} = {A, B, D, E, G, H, I, O}
Step 4: Calculate (A ∪ B) - (A ∪ C)
(A ∪ B) - (A ∪ C) = {A, B, C, D, E, G, I} - {A, B, D, E, G, H, I, O} = {A, B, D, E, G, I}
Result:
A ∪ (B ∩ C) = {A, B, D, E, G, I}
(A ∪ B) - (A ∪ C) = {A, B, D, E, G, I}
After following the process and checking intersections, unions, and differences, we conclude that the given statement is true:
A ∪ (B ∩ C) = (A ∪ B) - (A ∪ C)