Quick answer: Union A ∪ B contains elements in A or B or both. Intersection A ∩ B contains only elements common to both. For finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
Worked example
Let A = {1, 2, 3, 4} and B = {3, 4, 5}. Find their union and intersection.
- Common elements are 3 and 4, so A ∩ B = {3, 4}.
- Collect each element once for A ∪ B = {1, 2, 3, 4, 5}.
- The count formula gives 4 + 3 − 2 = 5.
Check the result
Elements 3 and 4 were counted in both original sets, explaining the subtraction.
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Common mistake to avoid
A set does not list duplicate elements. In a Venn diagram, place common elements in the overlap before filling the outer regions.
Try it yourself
1. Of 20 students, 12 study French, 9 German and 4 both. How many study either? 2. How many study neither?
Answers and reasoning
1. 12 + 9 − 4 = 17. 2. 20 − 17 = 3; this uses the stated total of 20.
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