==> The number of positive integers divisible by 7 but not by 11<span> is </span>142<span> - </span>12<span> = 130. ==>the number of positive integers less than 1000 that are divisible by either 7 or </span>11<span>is </span>142<span> + </span>90<span> - </span>12<span> = </span>220<span>. ==>the number of positive integers less than 1000 that are divisible by exactly by one of 7 and </span>11<span> is </span>220<span> - </span>12<span> = </span>208<span>.</span>