Symbols:Set Theory/Symmetric Difference

Symmetric Difference

$\symdif$

The symmetric difference between two sets $S$ and $T$ is denoted $S \symdif T$ and consists of all the elements in either set, but not in both.

$S \symdif T := \paren {S \setminus T} \cup \paren {T \setminus S}$

The $\LaTeX$ code for \(\symdif\) is \symdif .

Also denoted as

There is no standard symbol for symmetric difference. The one used here, and in general on $\mathsf{Pr} \infty \mathsf{fWiki}$:

$S \symdif T$

is the one used in 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics.

The following are often found for $S \symdif T$:

$S * T$

$S \oplus T$

$S + T$

$S \mathop \triangle T$

According to 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: symmetric difference:

$S \mathop \Theta T$

$S \mathop \triangledown T$

are also variants for denoting this concept.

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.): symmetric difference recognizes a further variant:

$S \mathop \nabla T$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols