Answer
For all sets A and B, (Bc ∪ (Bc − A))c = B.
(Bc ∪ (Bc − A))c = (B ⋂ (Bc − A)c) (by DeMorgan’s law)
= (B ⋂ (Bc ⋂ Ac)c) (by definition of set difference)
= (B ⋂ (B ⋃ A)) (by DeMorgan’s law)
= B (by Absorption law)
Work Step by Step
(Bc ∪ (Bc − A))c = (B ⋂ (Bc − A)c) (by DeMorgan’s law)
= (B ⋂ (Bc ⋂ Ac)c) (by definition of set difference)
= (B ⋂ (B ⋃ A)) (by DeMorgan’s law)
= B (by Absorption law)