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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
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.

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