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Out of 500 car drivers, 400 are the owne...

Out of 500 car drivers, 400 are the owners of Maruti and 200 are the owners of Hundai. If 50 are the owners of both, then find the whether the datas are correct or not ?

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To determine whether the data provided is correct, we can use the principle of inclusion-exclusion in set theory. ### Step-by-Step Solution: 1. **Define the Sets**: Let: - \( M \) = Set of Maruti owners - \( H \) = Set of Hyundai owners 2. **Given Data**: - Total number of car drivers = 500 - Number of Maruti owners \( |M| = 400 \) - Number of Hyundai owners \( |H| = 200 \) - Number of owners of both Maruti and Hyundai \( |M \cap H| = 50 \) 3. **Apply the Inclusion-Exclusion Principle**: According to the principle, the total number of unique car drivers who own either Maruti or Hyundai (or both) can be calculated as: \[ |M \cup H| = |M| + |H| - |M \cap H| \] Substituting the values: \[ |M \cup H| = 400 + 200 - 50 \] 4. **Calculate**: \[ |M \cup H| = 400 + 200 - 50 = 550 \] 5. **Compare with Total Drivers**: We have calculated that there are 550 unique car drivers who own either Maruti or Hyundai. However, the total number of car drivers is given as 500. 6. **Conclusion**: Since 550 (the calculated unique owners) is greater than 500 (the total number of car drivers), the data provided is inconsistent. Therefore, the data is incorrect. ### Final Answer: The data is incorrect because the total number of unique car drivers owning either Maruti or Hyundai exceeds the total number of car drivers.
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