Answer:
(a) {1, 2, 5, 6}
(b) {3, 4, 7, 8}
(c) {1, 2, 3, 4, 5, 6, 7, 8}
(d) {1, 2, 7, 8}
Step-by-step explanation:
Given sets,
A = {1, 2, 3, 4}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8},
(a) Since, A Δ B = (A\B)∪(B\A) = all elements of A\B and B\A
∵ A\B = elements of set A which are not in B
= {1, 2}
And, B\A = {5, 6}
So, A Δ B = {1, 2, 5, 6}
(b) B\C = {3, 4},
C\B = {7, 8}
⇒ B Δ C = (B\C)∪(C\B) = {3, 4, 7, 8}
(c) A\C = {1, 2, 3, 4},
C\A = {5, 6, 7, 8},
⇒ A Δ C = (A\C)∪(C\A) = {1, 2, 3, 4, 5, 6, 7, 8}
(d) (A Δ B)\C = {1, 2}
C\(A Δ B) = {7, 8}
A Δ C = ((A Δ B)\C)∪(C\(A Δ B)) = {1, 2, 7, 8}
