Question

If A and B are two sets, then ((A' ∪ B') – A)' is equal to ____________.

Answer 1

For sets A and B, ((A' ⋃ B') – A)'
= ((A' ⋃ B') ∩ A')'
= ((A ∩ B)' ∩ A') ' (using De-Morgan's Law)
= (((A ∩ B)' )' ⋃ (A')') (using De-Morgan's Law)
= ((A ∩ B) ⋃ A)
= A
i.e ((A' ⋃ B') – A)' = A