Neither egg nor meat – count pure vegetarians via union: In a town of 5000 people, 3200 eat eggs, 2500 eat meat, and 1500 eat both egg and meat. How many are pure vegetarians (eat neither egg nor meat)?

Introduction / Context:
To find those who eat neither of two categories, compute the size of the union (eat at least one) and subtract from the total population.

Given Data / Assumptions:

• Total = 5000
• Egg eaters = 3200
• Meat eaters = 2500
• Both = 1500

Concept / Approach:
|Egg ∪ Meat| = 3200 + 2500 − 1500 = 4200. Pure vegetarians are the complement in the population.

Step-by-Step Solution:
Neither = 5000 − 4200 = 800

Verification / Alternative check:
Sum of disjoint parts: Only-egg (1700) + Only-meat (1000) + Both (1500) + Neither (800) = 5000.

Why Other Options Are Wrong:
600, 850, 900 do not align with the union computation.

Common Pitfalls:
Forgetting to subtract the overlap when computing the union.

Final Answer:
800