1.1 With pictures and words, describe each symmetry in D3 (the set of symmetries on an
equilateral triangle).
There are six symmetries: Three rotations of 0, 120, and 240, and ips over threedi erent
axes, each going through one vertex and the midpoint of

Reading Quiz 3
Consider the group Z10
That is the set of equivalence classes on Z where a is equivalent to b if a b
mod 10.
1. [1] What is the order of Z10
10
2. [1] What is the order of [2] (i.e. the equivalence class of 2) in Z10
The element 9 has order

Reading Quiz 3
Consider the group Z10 .
That is the set of equivalence classes on Z where a is equivalent to b if a b mod 10.
1. [1] What is the order of Z10 ?
2. [1] What is the order of [2] (i.e. the equivalence class of 2) in Z10 ?
3. [1] Find a subgro

1. 10
2. The element 9 has order 2
3. The group is cyclic. It has three proper subgroups: the trivial subgroup cfw_[0] (generated
by [0]), a cyclic subgroup of order 2 cfw_[0], [5] (generated by [5]), and a cyclic subgroup of
order 5 cfw_[0], [2], [4], [6

1.1 With pictures and words, describe each symmetry in D3 (the set of symmetries on an
equilateral triangle).
There are six symmetries: Three rotations of 0, 120, and 240, and ips over threedi erent
axes, each going through one vertex and the midpoint of

Reading Quiz 0
1. [3] True/False: If the statement is always true, give a brief explanation of why it is
(not a formal proof!). If the statement is false, give a counterexample.
(a) 8 | 56
(b) gcd(23 32 52 11 295 , 2 33 11 293 ) = 2 32 52 11 293
(c) lcm(2

Reading Quiz 0&2
1. [2] Create an equivalence relation on the set cfw_0, a, b, c.
Identify all the equivalence classes.
2. [1] Give an example of a set and binary operator that does not form a group.
Explain what group properties are not met.
3. [2] Consi

2,8*,11,12,22 top row
Heather Gudaz worked with Kevin
Math 402
2. Write out a complete Cayley table for D3.
8. In Dn, explain geometrically why a rotation and a reflection taken together in either order
must be a reflection.
Geometrically, well describe D

Reading Quiz 0
1. [3] True/False: If the statement is always true, give a brief explanation of why it is
(not a formal proof!). If the statement is false, give a counterexample.
(a) 8 | 56 -my computer cant understand the symbol used so I do not know what

2,8*,11,12,22 top row
Heather Gudaz worked with kevin
Math 402
2. Write out a complete Cayley table for D3.
8. In Dn, explain geometrically why a rotation and a reflection taken together in either order
must be a reflection.
Geometrically, well describe D

Reading Quiz 0 & 2
1. [2] Create an equivalence relation on the set cfw_0, a, b, c.
Identify all the equivalence classes.
2. [1] Give an example of a set and binary operator that does not form a group.
Explain what group properties are not met.
3. [2] Con