Question

The symmetric difference of sets a = {1, 2, 3, 4, 5, 6, 7, 8} and b = {1, 3, 5, 6, 7, 8, 9} is

Answer 1

Answer:

1. If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 3, 5, 6, 7, 8, 9}, then A – B = {2, 4}, B – A = {9} and A △ B = {2, 4, 9}.

Symmetric Difference Venn Diagram

Therefore, the shaded part of the Venn diagram represents A △ B = {2, 4, 9}.

Answer 2

Answer:

The symmetric difference of sets a and b = {2, 4, 9}    

Step-by-step explanation:

Given sets   a = { 1, 2, 3, 4, 5, 6, 7, 8 }

                   b =  { 1, 3, 5, 6, 7, 8, 9 }      

The formula for symmetric difference of sets A and B is given by

            ⇒ A Δ B = (A - B) U (B - A)  

The symmetric difference of sets a and b is

            ⇒ a Δ b = (a - b) U (b - a)

 a - b = { 1, 2, 3, 4, 5, 6, 7, 8 } - {1, 3, 5, 6, 7, 8, 9 } = { 2, 4}

 b - a = { 1, 3, 5, 6, 7, 8, 9} - { 1, 2, 3, 4, 5, 6, 7, 8} = {9}  

 ⇒ a Δ b = (a - b) U (b - a)  = {2,4} U {9} = {2, 4, 9}