Sets & Venn Diagrams
Enumerate sets and their unions and intersections systematically using tables, grids, and Venn diagrams to organise and count outcomes
What a learner can do afterwards
- List the elements in the union and intersection of two sets using a Venn diagram
- Use a two-way table to enumerate all possible outcomes of two combined events
- Shade regions of a Venn diagram to represent A ∪ B, A ∩ B, and A′ (complement)
1 · Read
A set is a group of things, like all your friends who play soccer. When you have two sets, you can draw them as two overlapping circles. That picture is called a Venn diagram. Where the circles overlap, you get things that belong to both sets. You have already counted the four regions of a Venn diagram: only A, only B, both, and neither. You also know about complementary events, things that are 'not this one.' A set works the same way: the complement of a set is everything outside its circle.
To list every outcome of two events, use a two-way table. For two dice, write the first die's numbers 1 to 6 down the side and the second die's numbers 1 to 6 across the top. Each cell is one pair, so there are 6 × 6 = 36 cells, with no pair missed and none repeated. To count the pairs with a total of 4, scan the cells: (1,3), (2,2) and (3,1). That is 3 outcomes out of 36.
Set A is numbers you say counting by 4, up to 24: {4, 8, 12, 16, 20, 24}. Set B is numbers you say counting by 6, up to 24: {6, 12, 18, 24}. The union, A ∪ B, lists every number in either set: {4, 6, 8, 12, 16, 18, 20, 24}. The intersection, A ∩ B, lists only the numbers in both sets: {12, 24}.
When you shade a Venn diagram: shade both whole circles for A ∪ B, shade only the middle overlap for A ∩ B, and shade everything outside a circle for its complement, A′.
A Venn diagram or a two-way table lets you list every outcome exactly once, so you can count unions, intersections, and complements without missing anything or doubling up.
Readings written for this dataset.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.