1. ## [SOLVED] Functions

How to determine this and please provide explanation if possible.

2. Originally Posted by ronaldo_07

How to determine this and please provide explanation if possible.
a. not $\displaystyle 1-1$, ie $\displaystyle 1 \mapsto 1$ and $\displaystyle 2 \mapsto 1$
b. yes, it is $\displaystyle 1-1$, easily can be checked, check $\displaystyle 0,1,2,3,4,5,6,7,8,9,10$.

3. Thank you could you explain it a bit further if possible please, how can you tell that 1 maps to 1 and 2 maps to 1.

4. Originally Posted by GaloisTheory1
a. not $\displaystyle 1-1$, ie $\displaystyle 1 \mapsto 1$ and $\displaystyle 2 \mapsto 1$
b. yes, it is $\displaystyle 1-1$, easily can be checked, check $\displaystyle 0,1,2,3,4,5,6,7,8,9,10$.
sure. a. not $\displaystyle 1-1$, ie $\displaystyle 1 \mapsto 1$ and $\displaystyle 2 \mapsto 1$ b/c $\displaystyle 1^3=1 \in \mathbb{Z}_7$ and $\displaystyle 2^3=1 \in \mathbb{Z}_7$

not onto. check $\displaystyle 0,1,2,3,4,5,6$

b. yes, it is $\displaystyle 1-1$, easily can be checked, check $\displaystyle 0,1,2,3,4,5,6,7,8,9,10$.

yes, it is onto. check $\displaystyle 0,1,2,3,4,5,6,7,8,9,10$.