ITPEC IP October 2025 Question 1
ITPEC IP October 2025 — Question 1 of 100
The intersection is always a subset of the union — every element common to both sets is necessarily present in at least one of them.
If an element belongs to A ∩ B, it belongs to A and to B. Therefore it satisfies the condition for membership in A ∪ B, which requires membership in A or B. This implication holds for every possible pair of sets, including empty sets.
Answer (c)
Why not others:
- (a) fails when A and B overlap, because intersection elements are also in the union rather than its complement
- (b) fails when B contains an element outside A
- (d) fails because every intersection element is in A, not in A's complement
Key rule: Intersection narrows membership and union broadens it, so A ∩ B ⊆ A ⊆ A ∪ B.
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