Know the symbols
= in both (intersection); = in either (union); = not in (complement); = the universal set; = the empty set; = the number of elements in .
Fill the overlap first
Always put the "both" (intersection) value in the centre first, then subtract to get the "only" regions; remember the region outside the circles.
Union formula
— subtract the overlap so it is not counted twice.
Drawn from real examiner reports.
n(...) is a count, not a list
Listing the elements (e.g. {4,7}) when asks for how many there are.
June 2024 Paper 2H (Q16c/d): values listed instead of counts.
Overlap not subtracted from a circle
Writing the full set total in the "only" region instead of subtracting those who are in both.
June 2024 Paper 2H (Q16): not taking the both-value away from the circle total.
Forgetting the region outside the circles
Omitting the elements in the universal set that are in neither nor .
June 2024 Paper 2F (Q15): values outside both sets omitted.
Guessing instead of shading
On set-notation questions, not shading the region asked for and so picking the wrong parts.
Nov 2024 Paper 2H (Q21): "very few used shading"; students guessed.
Union and intersection swapped
means in BOTH sets; means in either set (or both). Mixing the symbols shades or counts the wrong region — union is the wider "or", intersection the narrower "and".
Complement includes the outside region
The complement means everything NOT in — that includes the elements in B only AND the elements outside both circles. Forgetting the outside region undercounts .
Shade the region the notation describes
Before reading values, shade exactly what the notation means — it stops you combining the wrong regions.
Every region sums to
All the separate regions of the Venn diagram — including the one outside the circles — must add up to , the size of the universal set. Use this total to find a missing region.
Work from the intersection outwards
Fill the "both" (intersection) region first, then subtract to get the "only" regions, then the outside. Building the diagram from the centre out stops you double-counting the overlap.
| Symbol | Meaning |
|---|---|
| intersection — in both and | |
| union — in or (or both) | |
| complement — not in | |
| the universal set (everything) | |
| the empty set (no elements) | |
| the number of elements in |
Note that is a count, not a list of the elements.
What does A ∩ B mean?
In a group of students, study French, study German and study both. How many study (a) French only, (b) neither subject?
