In a survey of 63 people, 23 people subscribed to magazine A, 21 people subscribed to magazine B, and 17 subscribed to magazine C. For any two of the magazines, 4 people subscribed to both magazines but not to the third magazine. If 18 people in the survey did not subscribe to any of the three magazines, how many people subscribed to all three magazines?

D
To count the number of elements in set A or B or C, find the sum of the members of each set, subtract from this sum the sum of the elements common to any two of these sets, and then subtract twice of the number of elements common to all three sets. If x represents the number of people who subscribe to all three magazines, the number of people who subscribe to magazine A or B or C is 23+21+17-(4+4+4)-2x or 49-2x Since 18 of the 63 people did not subscribe to any of the three magazines, 45 people subscribed to magazine A or B or C. Hence, 45 = 49-2x, so x = 2.