Sets
Sets and subsets, the operations ∪, ∩, ∖ and the complement, counting with Venn diagrams, and Cartesian products. Sets is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 4 lessons, each with the rule that solves it and a diagram.
Sets, elements and subsets
A set is given by listing its elements or by a property; order and repetitions do not matter. ∈ links an element to a set, ⊆ a set to a set. A set with n elements has 2ⁿ subsets, including ∅ and the set itself.
Operations on sets
A ∪ B: in A or in B; A ∩ B: in both; A ∖ B: in A but not in B; A′: in the universe but not in A. De Morgan: (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′. Draw two circles and shade.
Counting with Venn diagrams
|A ∪ B| = |A| + |B| − |A ∩ B|. Fill the diagram from the inside out: the overlap, then the “only” regions, then the outside. With three sets, add the single sets, subtract the pairs and add back the triple overlap.
Cartesian product
A × B is the set of ordered pairs (a, b) with a ∈ A and b ∈ B, and |A × B| = |A| · |B|. Order matters: (1, 2) ≠ (2, 1). The plane is ℝ × ℝ, and pairs with a condition are counted on the grid of all pairs.
What is the Bocconi Test format?
Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.
- Questions / time
- 50 / 75 minutes
- Distribution
- 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
- Scoring
- +1 correct · 0 blank · −0.2 wrong
- Question languages
- English · Italian
- Three-option questions
- Some critical thinking questions have three options; a wrong answer there costs −0.33
- Minimum score
- Below 17 points the test is not considered for selection
- AI degree
- Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
- Law test
- A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring
Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)
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