Mod-2 Function of A: Is it a Permutation?

[Ilikecereal]

4. Definition: A bijection from a set A to itself is called a permutation of A.

(i) Let A = {0, 1, 2, 3, 4} and let f : A -> A be the mod-2 function.
Is f a permutation of A? Justify your answerCan somebody explain how to find a mod-2 function for A? I know that a mod-2 function is basically the remainder of the input and 2.

Can't figure this out.

 

[pasmith]

4. Definition: A bijection from a set A to itself is called a permutation of A.

(i) Let A = {0, 1, 2, 3, 4} and let f : A -> A be the mod-2 function.
Is f a permutation of A? Justify your answer


Can somebody explain how to find a mod-2 function for A? I know that a mod-2 function is basically the remainder of the input and 2.

You have answered your own question: the mod-2 function gives you the remainder when the argument is divided by 2.

 

[HallsofIvy]

0 (mod 2)= ?
1 (mod 2)= ?
2 (mod 2)= ?
3 (mod 2)= ?
4 (mod 2)= ?

As you said, divide each by 2:
0 divided by 2= 0 with remainder 0.
1 divided by 2= 0 with remainder 1.
2 divided by 2= 1 with remainder 0.
3 divided by 2= 1 with remainder 1.
4 divided by 2= 2 with remainder 0.