MathAlgebraGroups

Introduction to groups

Set of subsets

Report a typo

Let $U$ be a non-empty set, $2^{U}$ the set of all subsets of $U$ , and $\triangle$ the operation on $2^{U}$ known as symmetric difference:

$A \triangle B = (A \cup B) \setminus (A \cap B)$

Set of subsets

Is $(2^{U}, \triangle)$ a group? Choose all correct statements.

Select one or more options from the list

\emptyset

is the identity

The associativity property holds

It is not a group

There is no identity

U

is the identity

The inverse of any

A \in 2^{U}

A

's complement

Some

A \in 2^{U}

don't have inverses

The inverse of any

A \in 2^{U}

A

itself

It is a group

___

Create a free account to access the full topic