Question 478443
The number of positive integers n less than 1000 that are divisible by 7:
[1000/7] = 142

The number of positive integers divisible by both 7 and 11 are those that are divisible by 77:
[1000/77] = 12

==> The number of positive integers divisible by 7 but not by 11 is 142 - 12 = 130.

The number of positive integers less than 1000 that are divisible by 11: 
[1000/11] = 90
==>the number of positive integers less than 1000 that are divisible by either 7 or 11 is 142 + 90 - 12 = 220.

==>the number of positive integers less than 1000 that are divisible by exactly by one of 7 and 11 is 220 - 12 = 208.