# Thread: logic sets help

1. ## logic sets help

can anyone do this question?

2. Hey

Do you know what Z6 means? What exactly is your question?

(1*1) mod 6 = 1
(1*2) mod 6 = 2
....
(1*5) mod 6 = 5

(2*1) mod 6 = (1*2) mod 6 = 2
(2*2) mod 6 = 4
(2*3) mod 6 = 6 mod 6 = 0
(2*4) mod 6 = 8 mod 6 = 2
(2*5) mod 6 = 10 mod 6 = 4

....

and so on.
Does it help?

Regards, Rapha

3. Hello, srk619!

Rapha is right . . .
You're expected to know what $\displaystyle \mathbb{Z}_6$ means.
If you don't, you shouldn't have been assigned this problem.

Give the multiplication table for $\displaystyle \mathbb{Z}_6$

and hence find all solutions to: .$\displaystyle x^2 \,=\,3\:\text{ in }\mathbb{Z}_6$ or explain why there are none.

. . $\displaystyle \begin{array}{c||c|c|c|c|c|c|} \times & 0&1&2&3&4&5 \\ \hline \hline 0 & 0&0&0&0&0&0 \\ \hline 1 & 0&1&2&3&4&5 \\ \hline 2 & 0&2&4&0&2&4 \\ \hline 3 & 0&3&0&3&0&3 \\ \hline 4 & 0&4&2&0&4&2 \\ \hline 5 & 0&5&4&3&2&1 \\ \hline\end{array}$

The values for $\displaystyle x^2$ are on the main diagonal,

. . where we see that: .$\displaystyle 3\cdot3 \:=\:3\text{ (mod 6)}$

Therefore: .$\displaystyle x = 3$

4. the question is part of Integers, Congruence arithmetic

its something like what is in the diagram