In a town with a population of 5000, 3200 people are egg-eaters, 2500 meat eaters and 1500 eat both egg and meat. How many are pure vegetarians?

Let, E be the set of people who are egg-eaters and M be the set of people who are meat-eaters.
As per given question,
n(E) = 3200, n(M) = 2500, n(E ∩ M) = 1500.
Use the formula
n(E ∪ M) = n(E) + n(M) – n(E ∩ M)
= 3200 + 2500 – 1500
= 5700 – 1500 = 4200.
∴ Number of pure vegetarians = n(U) – n(E ∪ M)
Number of pure vegetarians = 5000 – 4200 = 800.