Comprehension

In the figure, the triangle stands for 'hardworking'; the circle stands for 'graduate'; the rectangle stands for 'rich' and the square stands for 'employed'. The numbers in different segments show the number of persons.

Question: 1

How many employed graduates are hardworking but NOT rich?

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Focus on interpreting “NOT” conditions carefully in Venn diagram or set-based problems. Exclude all subsets related to the excluded category.

Updated On: Apr 23, 2025

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The Correct Option is D

Solution and Explanation

Using the Venn diagram or data table, we identify the region that represents graduates who are both employed and hardworking but **not** rich. This number is **8**.

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Question: 2

How many hardworking graduates are either rich or employed but NOT both?

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Use the formula for symmetric difference: \[ A \oplus B = (A \cup B) - (A \cap B) \] to solve "either but not both" questions.

Updated On: Apr 23, 2025

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The Correct Option is A

Solution and Explanation

We are looking for the number of hardworking graduates who are either rich or employed, but **not both**. Use the formula: \[ \text{(Rich ∪ Employed) – (Rich ∩ Employed)} \] within the hardworking set. The count for such individuals is **15**.

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