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Union, intersection, difference, symmetric difference, and Cartesian product of two comma-separated sets, with cardinalities and capped pair display.
Execution
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Tool usage guide
Perform core discrete mathematics set operations on two comma-separated lists, including Union (A ∪ B), Intersection (A ∩ B), Difference (A − B), Symmetric Difference (A △ B), and Cartesian Product (A × B), with automatic deduplication and calculated set cardinalities.
Background
A student is working on discrete mathematics problem sets involving non-overlapping set elements.
Problem
Calculate the symmetric difference between two numeric sets containing overlapping values.
How to use
Input '1, 2, 3, 4' into Set A, '3, 4, 5, 6' into Set B, and select 'Symmetric difference A △ B'.
Outcome
Returns A △ B = {1, 2, 5, 6} with cardinality |A △ B| = 4, omitting common elements 3 and 4.
Background
A manager needs to identify all attribute combinations for a two-tier product option set.
Problem
Create all possible pairings between available sizes and colors.
How to use
Input 'S, M, L' into Set A, 'Red, Blue' into Set B, and select 'Cartesian product A × B'.
Outcome
Produces 6 ordered pairs {(S, Red), (S, Blue), (M, Red), (M, Blue), (L, Red), (L, Blue)} with |A × B| = 6.
Yes, element comparisons are case-sensitive, meaning 'abc' and 'ABC' are treated as separate elements.
Duplicate values within the same input set are automatically collapsed, keeping only the first occurrence.
Difference (A − B) extracts elements exclusive to Set A, while Symmetric Difference (A △ B) keeps elements that belong to either Set A or Set B, but not both.
It generates all ordered pairs (a, b) where each element from Set A is combined with every element from Set B.
Cardinality, written as |A| or |B|, indicates the total count of unique elements in that set.