==> 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 either 7 or 11is 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.