Kenneth Rosen Edition 7 Exercise 2.2 Question 32 (Page No. 137)

Question

Find the symmetric difference of $\left \{ 1,3,5 \right \}$ and $\left \{ 1,2,3 \right \}.$

Answer 1

• $A\triangle B = A\oplus B =  (A\cup B) - (A\cap B) $
• $A\triangle B = A\oplus B =  (A - B) \cup  (B - A) $

Let $A = \left\{1,3,5\right\}$ and $B = \left\{1,2,3\right\}$ 

$A\triangle B  = \left [ \left\{1,3,5\right\} - \left\{1,2,3\right\} \right ] \cup \left [ \left\{1,2,3\right\} - \left\{1,3,5\right\} \right ]$

$A\triangle B  = \left\{5 \right\} \cup \left\{2 \right\} = \left\{5,2\right\}$

Answer 2

A symmetric difference B  = (A U B) – (A intersection B)

which is equal to {2,5}.