The symmetry group of a pattern always has: I: the identity element
II: an even number of elements
A) I only
B) II only
C) I and II
D) neither I nor II

Question

Quizplus · Accepted Answer

The symmetry group of a pattern always includes the identity element, which is the operation of doing nothing to the pattern, leaving it unchanged. This is a fundamental property of all groups in mathematics, not just symmetry groups. The statement about having an even number of elements is not true for all symmetry groups; some symmetry groups can have an odd number of elements.

The Symmetry Group of a Pattern Always Has: I: the Identity