Purchase Solution

Associative and Commutative Rule

Not what you're looking for?

Ask Custom Question

Prove that addition modulo n, written +n is:
1) associative
2)comutative

there are two ways to prove these properties. each way requires a definition or two:
1) for n≥2, 0≤a, b≤n+1
a+n(written as a power in a corner downside, but dont know how to put it tho) b={condition 1 - a+b if a+b<n;condition 2 - a+n-n if a+b>or=n}

2) writing an(n is written as a power at the corner downside) for a mod n and (a+b)n(little n at the corner)=a+n(little n at the corner downside)b, then
(p+nq)&#8801;(Pn+qn)n (again n is written as a power at the corner but down the side not on the top)
Do the proofs using both methods. which is more algebraic?

I need you to go through the proof, step by step with me in this question, and how to apply these condition to the two methods of proving.

Purchase this Solution

Solution Preview

I'm going to type up the mathematical part of the answer in Microsoft Word and attach it separately. The basic vitally important definitions are here.

Please let me know if it comes through OK because I'm new to this system and want to make sure everything works out all right -- there's some way here you can drop a message, I think (if nothing else works, try tos end a problem with zero credits and put my name on it)

OK, two very important basics.

Commutatitive and Associative:

To COMMUTE means to drive back and forth -- for example, your dad or your neighbour commutes to work, ie he/she drives in and out every day. So the commutative law has to do with going back and forth, reversing direction.
In basic arithmetic, we use this all the time without thinking about it:
5 + 9 = 9 + 5 , a + b = b + a (commutative law of addition)
5 x 9 = 9 x 5 , ab = ba (commutative law of multiplication)

Note that some things are NOT commutative -- you can't change order in subtraction or in division, right?
NOT correct: 9 - 5 X=X 5 - 9 (using X=X to mean NOT equal
2/4 X=X 4/2

Also if you have learned matrices, matrix multiplication is NOT commutative, you can;t change the order. It's the fact that some things work and some things don't that make it important to study when the property works and when it doesn't.

To ASSOCIATE means to get together in groups. You associate with your friends. Your co-workers my also be called your associates. So the ...

Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.