Mathematical logic and foundations Definition

Symmetric difference

Definition

Let $A$ and $B$ be sets. The symmetric difference of $A$ and $B$ is the set $A \mathbin{\triangle} B = (A \setminus B) \cup (B \setminus A).$ An object $x$ is an element of $A \mathbin{\triangle} B$ when $x$ is an element of exactly one of $A$ and $B$ .

Remarks

Another notation is $A \ominus B$ . Example: $\{1, 2, 3\} \mathbin{\triangle} \{2, 3, 4\} = \{1, 4\}$ . Also $A \mathbin{\triangle} B = (A \cup B) \setminus (A \cap B)$ . The power set of a set is a group under symmetric difference, with identity $\varnothing$ .

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Element definition
Proposition concept
Set definition
Disjunction definition
Negation definition
Union definition
Set difference definition
Symmetric difference definition

Tag	`0Z49NTR1DZ`
URI	`m2://0Z49NTR1DZ`
Kind	definition
Writing	W1 stated
MSC	03E20
Defines	Symmetric difference
Uses	Set difference, Union

Symmetric difference

Definition

Remarks

Reading path

Further reading

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