Answer
Proof: Suppose A and B are any sets and A ⊆ B. [We must show that A⋃B⊆B .] Let x ∈ A⋃B . [We must show that xϵB.] By definition of union, x ∈ A or x ∈ B . In case x ∈ A , then since A ⊆ B, x ∈ B . In case x ∈ B, then clearly x ∈ B. So in either case, x ∈ B [as was to be shown]
Work Step by Step
Proof: Suppose A and B are any sets and A ⊆ B. [We must show that A⋃B⊆B .] Let x ∈ A⋃B . [We must show that xϵB.] By definition of union, x ∈ A or x ∈ B . In case x ∈ A , then since A ⊆ B, x ∈ B . In case x ∈ B, then clearly x ∈ B. So in either case, x ∈ B [as was to be shown]
