Meaning of the symbol $\oplus$

Question

Anybody who knows/can explain what this character means?

It tells you it's the symmetric set difference. – Karl Feb 26 '17 at 10:20 — Karl, Feb 26 '17 at 10:20

score 3 · Accepted Answer · answered Feb 26 '17 at 10:22

3

The symbol is symmetric set difference,
$A \oplus B = (A-B) \cup (B-A)$.
The red colour portion shows the symmetric difference.

answered Feb 26 '17 at 10:22

Isha Tarte

score 0 · Answer 2 · answered Feb 26 '17 at 10:20

This is symmetric difference:

$$A \oplus B:=(A-B) \cup (B-A).$$

It is the collection of elements in either of the sets, but not the intersection. Associativity is probably easiest using:

$$(A-B) \cup (B-A)=(A \cap B^c)\cup (A^c \cap B),$$

Where $A^c$ denotes the set theoretic complement.

2 Answers2