We know that Union of two sets: The union of two sets A and B ,written as A ∪ B ,is the set consisting of all the elements which are either in A or in B or in both, thus, A ∪ B = {x: x∈ A or x ∈ B} Clearly, x ∊ A ∪ B ⇒ x ∊ A or x ∊ B, and x ∉ A ∪ B ⇒ x ∉ A and x ∉ B. some important results on operations on sets A ⊆ A ∪ B , B ⊆ A ∪ B , A ∩ B ⊆ A , A ∩ B ⊆ B It is given that A∪B = A, and B∪C = B A∪B = A ⇒ B⊂A, and B∪C = B ⇒ C⊂B ⇒ C⊂A (∵ B⊂A) ⇒ A∪C = A Therefore, Let A∪B = A and B∪C = B. Then A∪C = A.