Question 1054668
Instead of names, let's use numbers.
1-January
2-February
.
.
.
11-November
12-December
So, if M=12, then M-1=11. True
If M-1=11, then M-6=M-1-5=11-5=6. True
If M-6=6, then M+1=M-6+7=6+7=13=1. True (the months repeat after 12 months so 13=1)
If M+1=13, then M+1-1=13-1=12. True