From the concepts mentioned about the symmetric difference, different properties can be deduced:
- The symmetric difference of a set with respect to itself is the empty set: A Δ B = Ø
- Therefore, the symmetric difference of a set A with the empty set is the same set A: A Δ Ø = A
- The symmetric difference of a set and one of its subsets is the difference between them: B ⊆ A → A Δ B= A B
- And the symmetric difference of the sets A Δ B and C is the same as that of the sets A Δ B and C. This is expressed: (A Δ B) Δ C = A Δ (B Δ C)
- Likewise, the symmetric difference of the sets A and B is equal to the symmetric difference of the sets B and A. Which is represented as follows: A Δ B = B Δ A
Bibliography
- Morra, J. Topic 11. Basic concepts of set theory. Algebraic structures . (2020, Kindle edition. Spain. B085WBRJNC.
- López Mateos, M. Sets, Logic and Functions. (2019, 2nd edition). Spain. Manuel Lopez Mateos.
- Uzcátegui Aylwin, C. An introduction to the descriptive theory of sets. (2020). Spain. Uniande Editions.
