Posted: Sun Sep 19, 2004 6:50 pm    Post subject: Basic Questions in the Algebra textbook

These are some basic questions in the textbook but I don’t know how to do and write the solutions clearly.

1. How to find all the solutions of in ,

where and is addition modulo 7?

2. Let

a. Illustrate, using A and B, why we consider 2+3=5. Use similar reasoning and with sets of your own choice to decide what you would consider to be the value of i. , ii. , where
b.Illustrate why we consider that 2 x 3 = 6 by plotting the points of A x B in the plane . Use similar reasoning with a figure in the text to decide what you would consider to be the value of .

Thank you.

Posted: Wed Sep 22, 2004 8:51 pm    Post subject:

1) .

That means there exists an integer n s.t. 3x + 7n = 5.

Using the extended Euclidean Algorithm gives .

That means x = 4 (in ).

2a)

I think that it is because 2 = |A|, 3 = |B|, . Anyway, and

b)

where “x” is the Catesian Product. And . Since is countable, its cardinality is . So .