boolean groupの例文

例文

1. Sometimes the Boolean group is actually defined as the symmetric difference operation on a set.
2. Equivalently, a Boolean group is an dimension is therefore equal to the number of elements of " X ".
3. The Klein four-group is also isomorphic to the direct sum, so that it can be represented as the pairs under component-wise addition elementary abelian 2-group, which is also called a Boolean group.
4. From the property of the inverses in a Boolean group, it follows that the symmetric difference of two repeated symmetric differences is equivalent to the repeated symmetric difference of the join of the two multisets, where for each double set both can be removed.
5. Taken together, we see that the power set of any set " X " becomes an abelian group if we use the symmetric difference as operation . ( More generally, any field of sets forms a group with the symmetric difference as operation . ) A group in which every element is its own inverse ( or, equivalently, in which every element has order 2 ) is sometimes called a Boolean group; the symmetric difference provides a prototypical example of such groups.