Question

Let A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {5, 6, 7, 8}. Find each of the following sets. (Enter your answers in set-roster notation.) (a) A Δ B (b) B Δ C (c) A Δ C (d) (A Δ B) Δ C

Answer 1

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}