We can solve this using the principle of inclusion-exclusion, a common method in set theory.

Let:

• $D$ represent the set of people who own a dog.
• $C$ represent the set of people who own a cat.
• The total number of surveyed people is 436.

We are given the following:

• 140 people own only a dog ($D - C$).
• 76 people own only a cat ($C - D$).
• 122 people own neither a dog nor a cat.

We need to find how many people own both a dog and a cat ($D \cap C$).

Step-by-step solution:

1. The total number of people who own a dog or a cat or both is: $436 - 122 = 314$ So, 314 people own either a dog, a cat, or both.

2. The total number of people who own only a dog or only a cat is: $140 + 76 = 216$

3. Let $x$ be the number of people who own both a dog and a cat. We know that the number of people who own either a dog or a cat (or both) is the sum of those who own only a dog, only a cat, and both a dog and a cat: $140 + 76 + x = 314$

4. Solving for $x$: $x = 314 - (140 + 76) = 314 - 216 = 98$

Conclusion:

98 people own both a dog and a cat.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. What is the total number of people who own a dog (including those who own both)?
2. How many people own a cat (including those who own both)?
3. What percentage of people own only a dog?
4. What percentage of the surveyed population own neither a dog nor a cat?
5. If 50 more people were surveyed and all owned a dog, how would this affect the total?

Tip: Always use diagrams like Venn diagrams for such set-related problems to visualize relationships easily.