Read pp 1-14. This should all be review. Be prepared to answer questions on those pages. The
following HW is a small sampling of the material in pp 1-14. It should get you started thinking about it.
Ill be glad to answer questions about this material but
Q1. The following table gives a list of a few different relations on various sets.
Which of the relations are transitive? reflexive? symmetric? equivalence? Mark an X in the column if that
relation is of the type indicated.
Q2. For those which are
Suppose that Z and W are two non-zero complex numbers. Can WZ be zero?
Let Z=a+bi and W=c+di Then ZW= ac-bd +(ad+bc) i .
Define: |Z|=a2+b2 and note |ZW| = |Z|W|
which we prove as follows.
We use squares which saves us constantly writing radical signs. The
HW2 Fall 2013 Abstract Algebra
You may work with at most two other people. Each person MUST write up their
own answers without their teammates being present. The answers wont be
exactly the same because they werent copied. Be sure your name appears and
Homework due Thursday November 29.
Be sure you give clear, convincing answers to each WHY? And be sure to carefully prove each
1. Prove that if H is a subgroup of G then then the mapping f:aHbH given by f(ah)=bh for all h in
H is a 1-1, onto map. (T