What is a Venn diagram? Explain the types of relationships it shows, with examples, and solve a survey problem.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Open in two lines. A Venn diagram uses circles inside a box to show how groups are related: inside, overlapping or separate. It is used both to choose the right figure and to count members.
2 · Draw the common types. [Diagram: nested circles (mango, fruit, food); two separate circles inside one (rice, wheat, cereal); two overlapping circles (women, doctors); separate circles (iron, wood)]
3 · Formulas.
Two groups: n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
Three groups: add the three, subtract the three pair values, add back the centre.
None = total − union.
4 · Fill from the middle.
Write the 'all three' value first.
Exactly two = pair value − centre.
Only one = circle total − the rest of that circle.
None = total − everything inside the circles.
5 · Worked survey example.
60 students: idli 30, dosa 25, pongal 20; idli and dosa 10, dosa and pongal 8, idli and pongal 6; all three 3.
Union = 30 + 25 + 20 − 10 − 8 − 6 + 3 = 54.
None = 60 − 54 = 6.
6 · Use in competitive exams. SSC, railway and placement tests ask 'which diagram' items and survey counts; bank papers use the same circles to check syllogisms.
7 · Close in one line. Choose the figure from the relationships, and count from the centre outwards.
Scoring tip: Draw and label the circles with the numbers in each region; a clear diagram often earns half the marks.
