The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false?
You're right 0,4,6 are missing ; so for every n mod 10 = {0,4,6} this set is definitely not closed. But trick is it is not closed is not false reason ; it's True.
Gatecse