# What are the properties of symmetric difference?

## What are the properties of symmetric difference?

In this entry, we list and prove some of the basic properties of △ . If A⊆B A ⊆ B , then A△B=B−A ⁢ ⁢ B = B – A , because A∪B=B A ∪ B = B and A∩B=A A ∩ B = A . A△∅=A ⁢ ⁢ , because ∅⊆A ∅ ⊆ A , and A−∅=A A – ∅ = A ….Proof.

Title properties of symmetric difference
Entry type Derivation
Classification msc 03E20

What is the symmetric difference between two sets?

‘Symmetric difference between any two sets is defined as a new set containing all the elements present in either of the sets but not in their intersection. ‘

### What is symmetric difference between two sets with example?

For an example of the symmetric difference, we will consider the sets A = {1,2,3,4,5} and B = {2,4,6}. The symmetric difference between these sets is {1,3,5,6}.

What is the difference between difference and symmetric difference?

Difference: Elements present on one set, but not on the other. Symmetric Difference: Elements from both sets, that are not present on the other.

#### What is the symbol of symmetric difference?

Δ
Symbol. The symbol of symmetric difference is “Δ” which is read as “delta” or “symmetric difference”. Therefore, “A Δ B” is read as “A delta B” or “set A symmetric difference set B”.

How is difference of two sets being defined?

If A and B are two sets, then their difference is given by A – B or B – A. • If A = {2, 3, 4} and B = {4, 5, 6} A – B means elements of A which are not the elements of B.

## What is the symmetric difference of three sets?

Closed 2 years ago. I learned that the symmetric difference of sets A,B is given by: A△B=(A−B)∪(B−A).

What is a ∆ B?

The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B. A △ B is the set of all those elements which belongs either to A or to B but not to both. A △ B is also expressed by (A ∪ B) – (B ∩ A).

### What does ∆ mean in sets?

The Δ in set theory is the symmetric difference of two sets. A Δ B = (B−A)∪(A−B)