In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Explanation

To find how many people liked product C only, we can use the principle of inclusion-exclusion and a Venn diagram to visualize the problem. Here’s the step-by-step solution:

### Step 1: Define the Sets
Let:
- \( A \) = Set of people who liked product A
- \( B \) = Set of people who liked product B
- \( C \) = Set of people who liked product C

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