ITPEC IP April 2022 Question 2
ITPEC IP April 2022 — Question 2 of 100
The intersection of A and B is always a subset of their union. If an element is in A ∩ B, it belongs to both A and B. It therefore certainly belongs to at least one of them, which is the membership condition for A ∪ B. Hence A ∩ B ⊆ A ∪ B for all sets.
Answer (c)
Why not others:
- (a) elements in the intersection also belong to the union, not to the complement of the intersection
- (b) the union can contain elements belonging only to B, so it need not be a subset of A
- (d) every intersection element is in A and therefore cannot also be in A's complement
Key rule: Intersection can only narrow membership; union can only broaden it, so intersection is contained in union.
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