Set operations describe how groups overlap and differ. This section has four lessons and a practice set, and belongs to the wider SPM Mathematics guide.
What does this section cover?
Begin with reading union, intersection and complement notation, which fixes what each symbol asks for. Next is solving two-set Venn diagram questions, where you learn to fill the overlap first.
Then comes solving three-set Venn diagram questions, with its seven regions. The last lesson, translating word statements into set notation, links sentences to symbols. The practice set mixes all four.
One class, three ways to ask
In a class of 30 students, 14 are in the netball team (N), 12 are in the choir (C) and 4 are in both.
| How the question is asked | What it needs |
|---|---|
| List N ∩ C | The names or numbers in both groups |
| Find n(N ∪ C) | 14 + 12 − 4 = 22 |
| How many are in neither? | (N ∪ C)′, which is 30 − 22 = 8 |
| Shade N′ ∩ C on a diagram | The choir-only region, 12 − 4 = 8 |
The same class supports a list, a count and a shaded region. That is why all four lessons connect.
Who should start where?
If you are new to Form 4, begin with notation and follow the order. If you can read the symbols but diagrams fail, start at the two-set lesson.
If two-set questions are fine and only three-set questions lose marks, go to the third lesson. Whichever you choose, check each diagram by adding every region and comparing with the total.
For a teacher to work on your diagrams with you, see online one-to-one Mathematics tuition.