For a universal set U, draw a Venn diagram for three sets A, B, and C, indicating the locations of the elements of U. If A, B, and C satisfy all the conditions below, determine A ∩ B ∩ C and U. Clearly list the sets A, B, C, and U by listing their elements in set notation.
A ∪ B ∪ C = {7}
A ∩ B ∪ C = {11, 12}
A ∪ B ∩ C = {1, 8}
B ∪ C ∩ A = {4, 6}
C ∪ A ∩ B = {3, 9, 10}
(B ∪ C) ∩ A = {3, 4, 5, 6, 9, 10}
(A ∪ C) ∩ B = {1, 2, 3, 8, 9, 10}
(A ∪ B) ∩ C = {14, 6, 8}
A =
B =
C =
U =