Fill in the boxes in the following proof by contradiction that: For all sets A and B, if B ⊆ A' then A ∩ B = Ø Proof: Let A and B be any sets with  B ⊆ A' and suppose that A ∩ B ≠ Ø That is, suppose there is an element x in __________ By definition of intersection, x ∈ ________ and x ∈   ________ By definition of subset, if  x ∈ B then x ∈  __________ and by definition of complement if x∈ A' then x∉ _________  In particular, x ∈ A and x ∉___________ , which is a contradiction. Hence the original supposition is false , and so if B ⊆ A' then A ∩ B = Ø as claimed.

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