In the universal set U, the symmetric difference of sets A and B is the set of elements belonging to either A or B but not both sets at the same time.
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”.
Property
By involving other operations on the sets, we can write:
A Δ B = (A ∪ B) \ (A ∩ B)
or:
A Δ B = (A ∩ B’) ∪ (A’ ∩ B)
Example
In the universal set U represented here, we have:
E Δ F = (E ∪ F) \ (E ∩ F) ={a, b, c, d, e, f, g, h, i, j, k} \{c, d, e} = {a, b, f, g, h, i, j, k}
