

InterviewSolution
Saved Bookmarks
1. |
Using properties of sets and their complements prove that:(i) (A ∪ B) ∩ (A ∩ B’) = A (ii) A - (A ∩ B) = A – B |
Answer» (i) (A ∪ B) ∩ (A ∩ B’) = A L.H.S = (A ∪ B) ∩ (A ∩ B’) = A ∪ (B ∩ B’) (By distributive law) = A ∪ ∅ (∴ B ∩ B’ = ∅) = A R.H.S. (ii) A - (A ∩ B) = A – B L.H.S = A - (A ∩ B) = A ∩ (A ∩ B)’ [∴ A – B = (A ∩ B)’] = A ∩ (A’ ∪ B)’ (By Demorgan's law) = (A ∩ A)’ ∪ (A ∩ B) (By distributive law) = ∅ ∪ A ∩ B’ (∴ A ∩ A’ = ∅) = A ∩ B’ = A – B = R.H.S |
|