Venn Diagrams
🔒 Log in to trackTwo question families: (1) region arithmetic — count union, intersection, only-regions, exactly-two, neither using inclusion-exclusion over labelled Venn regions; (2) relation selection — decide whether categories nest (definitional necessity), stay apart (impossibility) or intersect (possible but not forced). The arithmetic family is pure formula discipline; the relation family is two quick tests per pair. Label every region before computing and both become near-90% accuracy topics.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
4 exam-level questions worked step by step.
55 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (55 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Two sets, find the rest
very commonTwo totals and the overlap are given. Asks for "neither", "only one" or "at least one".
At least one = A + B − both.
Neither = total − at least one.
In a class of 60, 35 like tea, 30 like coffee and 10 like both. How many like neither?
At least one = 35 + 30 − 10 = 55
Neither = 60 − 55
= 5
Two sets, find the overlap
commonThe group size and both circle totals are given. Asks how many are in both.
Both = A + B − total (when everyone is in at least one).
Draw a box with four parts to check.
In a class of 80, everyone plays chess or carrom. 50 play chess and 40 play carrom. How many play both?
Add: 50 + 40 = 90
That is 10 more than 80, because those who play both are counted twice
Both = 10
Sets in percent
commonThe data is in percent.
Take the total as 100.
Solve in percent, then change to people if asked.
70% watch cricket, 60% watch football and 40% watch both. What percent watch neither?
At least one = 70 + 60 − 40 = 90%
Neither = 100 − 90
= 10%
Largest or smallest overlap
occasionalThe overlap is not given. Asks the maximum or minimum.
Maximum overlap = the smaller set.
Maximum "neither" happens when the smaller set is inside the bigger one.
In a group of 80, 50 like cricket and 40 like hockey. What is the maximum number who like neither?
For most in neither, the overlap should be biggest
Put all 40 hockey fans inside the 50 cricket fans
Neither = 80 − 50 = 30
Three sets, at least one or none
very commonThree totals, three pair overlaps and the triple overlap are given.
At least one = sum of totals − sum of pairs + triple.
None = total − at least one.
Out of 200 people, 90 drink coffee, 80 tea and 70 milk. Pairs: 40, 35 and 30. All three: 15. How many drink none?
Totals: 90 + 80 + 70 = 240
Pairs: 40 + 35 + 30 = 105
At least one = 240 − 105 + 15 = 150
None = 200 − 150 = 50
Exactly two of three
commonAsks for "exactly two", "exactly one" or "at least two" in a three-set problem.
Exactly two = sum of pairs − 3 × triple.
At least two = sum of pairs − 2 × triple.
Pairs overlap by 8, 7 and 6 people. All three overlap by 3. How many are in exactly two sets?
Sum of pairs = 8 + 7 + 6 = 21
The triple group is counted 3 times in it: 3 × 3 = 9
Exactly two = 21 − 9 = 12
Numbers written in each part
commonA diagram has a number in each part and the question describes a group in words.
List the parts that match the words.
Add each part once.
Only N: 20, only T: 25, only R: 5, N and T only: 15, T and R only: 6, N and R only: 4, all three: 10. How many use exactly one source?
"Exactly one" means the "only" parts
20 + 25 + 5
= 50
Pick the right diagram
very commonThree words are given and the options are circle pictures.
Compare the words two at a time.
Decide if they are separate, inside one another, or overlapping.
Which diagram fits: Even numbers, Odd numbers, Prime numbers?
Even and odd numbers never overlap
2 is even and prime; 3 is odd and prime
So prime overlaps both: two separate circles with a third circle touching both