Intuition behind inclusion-exclusion principle for three sets

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For two non-disjoint sets AA and BB, A+B|A| + |B| would involve counting AB|A \cap B| twice. The following diagram shows how many times each region in Venn diagram is counted for A+B|A| + |B|.

Venn diagram for two sets

The question below is about three non-disjoint sets AA, BB and CC. Match the following diagrams to the correct expression. Like the diagram above, the ones below show how many times each region is counted.

  1. Venn diagram for three sets (1)

  2. Venn diagram for three sets (2)

  3. Venn diagram for three sets (3)

Match the items from left and right columns
1
2
3
A+B+CABACBC+ABC|A| + |B| + |C|- |A \cap B| - |A \cap C| -|B \cap C| + |A \cap B \cap C|
A+B+CABACBC|A| + |B| + |C|- |A \cap B| - |A \cap C| -|B \cap C|
A+B+C|A| + |B| + |C|
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