In the given diagram, the triangle represents Teachers, the circle represents Engineers, the square represents French speakers, and the rectangle represents Musicians. Find the total number of Teachers who can speak French and are also Engineers, and the number of Musicians who can speak French but are not Engineers
39
Triangle = Teachers, circle = Engineers, square = French speakers, rectangle = Musicians.
Teachers who speak French and are Engineers = region common to triangle, circle and square = 18
Musicians who speak French but are not Engineers = region common to rectangle and square, outside the circle = 21
Total = 18 + 21
= 39
Check: The 18 lies inside all of the triangle, circle and square, and the 21 lies only in the square and rectangle overlap.
Hence, 39.
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A research institute plans to recruit personnel for various positions based on the following criteria.
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(ii) Technicians who are either Botanists or Physicists but not Managers.
Find the number of people in the Venn diagram who are eligible according to the criteria.

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This question contains three categories. These categories may or may not be linked to one another. Each category may fit into one of the diagrams given below in the options. Select the diagram which most aptly represents the relationship among the given categories.
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