2. Let A = {0, 1, 2, 3, 4, 5}, B = {2, 4, 6, 8} and C = {1, 3, 5, 7}
Verify (A ∪ B) ∪ C = A ∪ (B ∪ C)
Solution:
(A ∪ B) ∪ C = A ∪ (B ∪ C)
L.H.S. = (A ∪ B) ∪ C
A ∪ B = {0, 1, 2, 3, 4, 5, 6, 8}
(A ∪ B) ∪ C = {0, 1, 2, 3, 4, 5, 6, 7, 8} ……………….. (1)
R.H.S. = A ∪ (B ∪ C)
B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
A ∪ (B ∪ C) = {0, 1, 2, 3, 4, 5, 6, 7, 8} ……………….. (2)
Therefore, from (1) and (2), we conclude that;
(A ∪ B) ∪ C = A ∪ (B ∪ C) [verified]
