Set intersection is a mathematical operation that finds the common elements between two or more sets.
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Learn about Set Intersection
A set intersection, described with the symbol ∩, describes the combination of two sets where the resulting set contains every element that can be found in both sets. Alongside unions and differences, set intersections are a primary method of interacting with and modifying sets. Sets and set theory in general are an important method to conceive of and visualize data, and are a common subject in mathematics and computer science courses.
Take the following sets, A and B. $$A = \{a, b, c, d\}$$ $$B = \{c, d, e, f\}$$The intersection of these two sets will contain every element that can be found in both sets. Each element will appear in the newly created set only once. $$A \cap B = \{c, d\}$$The resulting set is the intersection of sets A and B.
$$\textbf{1) Problem: \{Ti, Mn, Ru, Pt, Mt, Ds, Rg\}} \cap \textbf{\{Rg, Cl, Ds, Se, Br\}}$$ $$\\$$The intersection of two sets is every element appearing in both sets. Combine both sets into one, leaving out any elements that are in only one set: {Ds, Rg}.$$\\$$The resulting set is the intersection.$$\\$$ $$\textbf{Answer: \{Ds, Rg\}}$$ $$\\$$ $$\textbf{2) Problem: \{Lettuce, Artichoke, Radish, Tomato\}} \cap \textbf{\{Apple, Tomato, Orange\}}$$ $$\\$$The intersection of two sets is every element appearing in both sets. Combine both sets into one, leaving out any elements that are in only one set: {Tomato}. The resulting set is the intersection. $$\\$$ $$\textbf{Answer: \{Apple, Artichoke, Lettuce, Orange, Radish, Tomato\}}$$ $$\\$$ $$\textbf{3) Problem: \{42, 28, 49, 93, 12, 23, 47\}} \cap \textbf{\{42, 93, 12, 23, 47\}}$$ $$\\$$The key to this problem is noticing that the second set is a complete subset of the first. In that case, the result of their intersection will be identical to the second set.$$\\$$ $$\textbf{Answer: \{42, 93, 12, 23, 47\}}$$ $$\\$$ $$\textbf{Problem:\{O, N, C, Fe\}} \cap \textbf{\{\}}$$ $$\\$$ The intersection of any set with the empty set will always be the empty set.$$\\$$ $$\textbf{Answer: \{\}}$$ $$\\$$
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