Construct and interpret Venn diagrams for two or three sets, use set notation for union, intersection and complement, and calculate probabilities from a Venn diagram (Higher tier).

What this dot point is asking

At Higher tier, WJEC asks you to construct and interpret Venn diagrams for two or three sets, to use set notation for union, intersection and complement, and to calculate probabilities directly from a completed Venn diagram. The key skill is filling in the regions correctly, in particular putting the intersection in first and subtracting it from each set's total so that no element is counted twice. Once the diagram is complete, probabilities are read off as a count of the relevant region over the total. It is examined on Unit 2.

Set notation

Three symbols describe the regions of a Venn diagram.

Reading these symbols correctly is half the topic: $\cap$ is the small overlap ("and"), while $\cup$ is the larger union ("or"). A useful memory aid is that the intersection symbol $\cap$ looks like a bridge joining only where the two sets meet, while the union symbol $\cup$ is a cup that holds everything from both sets. Combinations such as $A \cap B'$ (in A but not B) and $(A \cup B)'$ (in neither) appear at Higher tier, and each names a single region of the diagram once you read the symbols carefully.

Filling in a Venn diagram

The order of filling matters, to avoid double counting.

So if $20$ like tea, $15$ like coffee and $8$ like both, then tea only is $20 - 8 = 12$ and coffee only is $15 - 8 = 7$; the overlap $8$ is counted once, not twice.

For three sets, the same principle applies but there are more regions: the central region (in all three) is placed first, then the three "two sets only" overlaps, then the three "one set only" regions, and finally anything outside all three. Working from the centre outwards, subtracting what is already placed at each stage, keeps every element counted exactly once even in the more crowded three-circle diagram.

Calculating probabilities

A completed diagram gives probabilities by counting.

The "neither" region is found by subtracting the union from the total: $25 - 14 = 11$ own neither.

Why this matters

Venn diagrams are a Higher-tier topic that organises overlapping events so probabilities of "and", "or" and "neither" can be read off cleanly, and they connect to the set notation used more widely in mathematics. The marks reward filling in every region accurately, with the intersection placed first to avoid double counting, and reading the correct notation ($\cap$ for the overlap, $\cup$ for the union, $A'$ for the complement). A completed Venn diagram makes otherwise fiddly combined-probability questions straightforward, which is why WJEC uses it for multi-step problems worth several marks.