ITPEC IP April 2018 Question 4
ITPEC IP April 2018 — Question 4 of 100
The intersection of two sets is always a subset of their union. Every element in A ∩ B belongs to both A and B, so it necessarily belongs to at least one of them and therefore lies in A ∪ B.
Answer (c)
Why not others:
- the union can contain elements from B that are not in A, so it is not always a subset of A
- elements in the intersection are inside A and B, not in their complements
- the union includes the intersection, so it cannot generally be contained in the intersection's complement
Key rule: For any sets A and B, A ∩ B ⊆ A ⊆ A ∪ B and A ∩ B ⊆ B ⊆ A ∪ B.
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