CLASS-11
SETS - SYMMETRIC DIFFERENCE OF TWO SETS

So,

(1)  A Δ B = (A ∪ B) – (B ∩ A)   

(2)   A Δ B = B Δ A      

(3)   A Δ A = φ,  A Δ φ  = A,  A Δ B = φ <=> A = B 

Example.1)  If A = {5, 6, 7, 8, 9, 10}, B = {5, 7, 9, 11}, then find A Δ B           

Ans.)    A Δ B = {6, 8, 10, 11}

Example.2) If A = {x ∈ R : 0 < x < 4}, and B = {x ∈ R : 1≤ x ≤ 7} then find A Δ B

Ans.)   A – B = {x ∈ R : 0 < x < 1},          

         B – A = {x ∈ R : 4 ≤ x ≤ 7}   

        A Δ B = (A – B) ∪ (B – A)  

                = {x ∈ R : 0 < x < 1} ∪ {x ∈ R : 4 ≤ x ≤ 7}

                = {x ∈ R, 0 < x < 1  or  4 ≤ x ≤ 7}