Symmetric Difference of Sets
The symmetric difference of sets P and Q is expressed as P Δ Q and defined as
P Δ Q = (P – Q) U (Q – P)
OR
P Δ Q = (P ∪ Q) – (P ∩ Q)
Venn Diagram of Symmetric Difference of Sets
In the Venn diagram below, the pink-shaded portion represents P Δ Q.
Example: If P = {4, 5, 6, 7, 8} and Q = {6, 7, 8, 10}, find P Δ Q.
Solution:
- Step – 1: Find P – Q.
P – Q = {4, 5, 6, 7, 8} – {6, 7, 8, 10} = {4, 5}- Step – 2: Find Q – P.
Q – P = {6, 7, 8, 10} – {4, 5, 6, 7, 8} = {10}- Step – 3: Find P Δ Q = (P – Q) U (Q – P).
P Δ Q = (P – Q) U (Q – P) = {4, 5} U {10} = {4, 5, 10}
Difference of Sets
Difference of Sets is the operation defined on sets, just like we can perform arithmetic operations on numbers in mathematics. Other than difference we can also perform union and intersection of sets for any given sets. These operations have a lot of important applications in mathematical practice. In this article, we will learn about the difference of sets including its definition, mathematical expressions, Venn diagram as well as properties of difference of sets. Let’s start our learning of the “Difference of Sets”.