55 792
Assignments Done
97,2%
Successfully Done
In December 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Abstract Algebra Question for Annemarie

Question #4997
Consider the function f : Z4 → Z12 defined by f(x) = 3x. Show that f(x) does
NOT preserve multiplication.
Expert's answer
f:Z4 --> Z12, f(x)=3x
We will show that this function does not preserve multiplication. we can consider x,y from Z4 such that
data:image/png;base64,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
let x=1, y=3 so we have:
f(1*3)=f(3)=9 (modulo 12)
f(1)*f(3)=3*9=27=3( modulo 12)
But 9 is not equal to 3 in Z12. So f does not preserve multiplication.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question