A survey was made about two daily newspapers, LOS ANGELES TIMES and THE NEW YORK TIMES, 105 people bought Los Angeles Times, 25 did not buy Los Angeles Times, 95 did not buy New York Times, while 83 bought Los Angeles times but not New York Times.

Question

A survey was made about two daily newspapers, LOS ANGELES TIMES and THE NEW YORK TIMES, 105 people bought Los Angeles Times, 25 did not buy Los Angeles Times, 95 did not buy New York Times, while 83 bought Los Angeles times but not New York Times. 
How many people took part in the survey?

jolly rancher · Answer

assuming there were no people in the survey population who did not respond to all questions, the population size would be

LAT + not-LAT = 105 + 25 = 130

because the two subsets are mutually exclusive, i.e., the intersection of those two subsets is empty

thus all members of the population must be contained in one or the other of those two subsets
the sum of those two sets is the total population