In a three-set Venn diagram, begin with the intersection of all three sets. Then subtract that number from each pairwise intersection to find the regions belonging to exactly two sets. Finish the single-set-only regions, then count outside. Example In a group of 30, n(A)=17,n(B)=13,n(C)=11. The inclusive pair counts are n(A B)=6,n(A C)=5,n(B C)=4, and 2 belong to all three. For example, A and B only contains 6-2=4. A only contains 17-4-3-2=8. The union contains 28, leaving 2 outside. The expression A B C means A and B but not C. It is one region, while (A B) C includes A only, B only and A-and-B only. A pairwise intersection includes the triple region unless “only” is stated.

In a three-set Venn diagram, begin with the intersection of all three sets. Then subtract that number from each pairwise intersection to find the regions belonging to exactly two sets. Finish the single-set-only regions, then count outside.

In a group of 30, \(n(A)=17,n(B)=13,n(C)=11\). The inclusive pair counts are \(n(A\cap B)=6,n(A\cap C)=5,n(B\cap C)=4\), and 2 belong to all three.

For example, A and B only contains \(6-2=4\). A only contains \(17-4-3-2=8\). The union contains 28, leaving 2 outside.

The expression \(A\cap B\cap C\prime\) means A and B but not C. It is one region, while \((A\cup B)\cap C\prime\) includes A only, B only and A-and-B only. A pairwise intersection includes the triple region unless “only” is stated.

Sets

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Counting with three overlapping sets

Counting with three overlapping sets