Note: In general X ∪ Y = {a: a ϵ X or a ϵ Y} 

X ∩ Y = {a:a ϵ X and a ϵ Y}. 

i. A ∪ B = {x: x ϵ A or x ϵ B} 

= {1, 2, 3, 4, 5, 6, 7, 8} 

ii. A ∪ C = {x: x ϵ A or x ϵ C} 

= {1, 2, 3, 4, 5, 7, 8, 9, 10, 11} 

iii. B ∪ C = {x: x ϵ B or x ϵ C} 

= {4, 5, 6, 7, 8, 9, 10, 11} 

iv. B ∪ D = {x: x ϵ B or x ϵ D} 

= {4, 5, 6, 7, 8, 10, 11, 12, 13, 14} 

v. A ∪ B = {x: x ϵ A or x ϵ B} 

= {1, 2, 3, 4, 5, 6, 7, 8} A ∪ B ∪ C 

= {x: x ϵ A ∪ B or x ϵ C} 

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} 

vi. A ∪ B = {x: x ϵ A or x ϵ B} 

= {1, 2, 3, 4, 5, 6, 7, 8} A ∪ B ∪ D 

= {x: x ϵ A ∪ B or x ϵ D} 

= {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14} 

vii. B ∪ C = {x: x ϵ B or x ϵ C} 

= {4, 5, 6, 7, 8, 9, 10, 11} 

B ∪ C ∪ D = {x: x ϵ B ∪ C or x ϵ D} 

= {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} 

viii. B ∪ C = {x: x ϵ B or x ϵ C} 

= {4, 5, 6, 7, 8, 9, 10, 11} 

A ∩ B ∪ C = {x:x ϵ A and x ϵ B ∪ C}. 

= {4, 5} 

ix. (A ∩ B) = {x:x ϵ A and x ϵ B}. 

= {4, 5} 

(B ∩ C) = {x:x ϵ B and x ϵ C} 

= {7, 8} 

(A ∩ B) ∩ (B ∩ C) = {x:x ϵ (A ∩ B) and x ϵ (B ∩ C)}. 

= ϕ 

x. A ∪ D = {x: x ϵ A or x ϵ D} 

= {1, 2, 3, 4, 5, 10, 11, 12, 13, 14}. 

B ∪ C = {x: x ϵ B or x ϵ C} 

= {4, 5, 6, 7, 8, 9, 10, 11} 

(A ∪ D) ∩ (B ∪ C) 

= {x:x ϵ (A ∪ D) and x ϵ (B ∪ C)}. 

= {4, 5, 10, 11}.