Question 4:
If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that
(i) (A ∪ B)΄ = A΄ ∩ B΄ (ii) (A ∩B)΄ = A΄∪ B΄
Answer
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8}, B = {2, 3, 5, 7}
(i) (A ∪ B)΄ = {2, 3, 4, 5, 6, 7, 8}΄ = {1, 9}
∴(A ∪ B)΄ = A΄∩ B΄
(ii) (A ∩ B)΄ = {2}΄ ={1, 3, 4, 5, 6, 7, 8, 9}
A΄ ∪ B΄ ={1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9}
∴(A ∩ B)΄ = A΄ ∪ B΄
Latest Govt Job & Exam Updates: