Sets and Venn diagrams
Objective. Use set notation, regions and complements.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Set notation describes collections of objects and how they overlap using symbols instead of words. A set is written with curly brackets, e.g. A = {2, 4, 6, 8}, and ∪ means union (everything in either set), ∩ means intersection (only what's in both), and A′ means the complement (everything outside A within the universal set ξ). Venn diagrams draw sets as overlapping circles inside a rectangle representing ξ, with each region holding the elements or the count that belongs only there. For example if ξ = {1,...,10}, A = even numbers, B = multiples of 3, then A ∩ B = {6} sits in the overlap, while A′ contains all the odd numbers. Reading a region correctly means checking every condition that applies to it, not just one.
Worked example
ξ = {1,2,...,12}, A = {multiples of 2}, B = {multiples of 3}. Find n(A ∩ B).
- 1List A = {2,4,6,8,10,12}
- 2List B = {3,6,9,12}
- 3Find common elements: A ∩ B = {6,12}
- 4Count them: n(A ∩ B) = 2
Answer: 2
Concept mastery
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Practice
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Start practisingCommon mistake. A common error is placing an element satisfying both conditions into only one circle instead of the overlap; e.g. putting 6 (even and a multiple of 3) in the 'even only' region loses it from A ∩ B, so always check all set conditions before placing a number.
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