In the diagram given below, triangle represents men, circle represents…
2023
In the diagram given below, triangle represents men, circle represents non-educated, square represents sports persons and rectangle represent married. How many non educated married women who are not sports persons are there?
- A.
6
- B.
7
- C.
8
- D.
9
Attempted by 122 students.
Show answer & explanation
Correct answer: B
Concept: A labelled Venn diagram assigns one set to each shape; a numbered region belongs to a set only if the region lies inside that shape's boundary, and it is excluded from a set if it lies outside that shape. To locate a region that must satisfy several conditions at once (some 'inside', some 'outside'), translate every condition into an inside/outside test against each shape, then keep only the region that passes every test simultaneously.
Application: Here triangle = men, circle = non-educated, square = sports persons, rectangle = married. The question needs a region that is non-educated (inside the circle) AND married (inside the rectangle) AND a woman, i.e. NOT a man (outside the triangle) AND NOT a sports person (outside the square). Checking the diagram's four candidate regions (6, 7, 8, 9) against all four conditions together:
Region | Inside circle (non-educated)? | Inside rectangle (married)? | Inside triangle (men)? | Inside square (sports person)? | Meets all 4 conditions? |
|---|---|---|---|---|---|
6 | No — outside the circle | No — outside the rectangle | Yes — inside the triangle (so these are men) | No — outside the square | Fails: not non-educated, not married, and is male |
7 | Yes — inside the circle | Yes — inside the rectangle | No — outside the triangle | No — outside the square | Passes every condition |
8 | No — outside the circle | Yes — inside the rectangle | No — outside the triangle | Yes — inside the square (so these are sports persons) | Fails: not non-educated, and is a sports person |
9 | Yes — inside the circle | No — outside the rectangle | No — outside the triangle | No — outside the square | Fails: not married |
Cross-check: Tracing the figure directly confirms this: region 7 sits in the sliver that lies inside both the circle and the rectangle, just to the right of the triangle's narrow apex sliver and outside the square's right edge — it is the only one of the four candidate regions inside both the circle and the rectangle while staying outside both the triangle and the square.
Answer: So the count of non-educated, married women who are not sports persons is 7.