What is Intersection and union? — Mathematics

Definition 1.7 High School Mathematics · Chapter 1 — Numbers and Sets of Numbers

Let $I$ and $J$ be two sets of real numbers. The intersection $I \cap J$ (“ $I$ and $J$ ”) is the set of numbers belonging to both; the union $I \cup J$ (“ $I$ or $J$ ”) is the set of numbers belonging to at least one of them.

Examples

Example 1.8

Take $I = \intcc{-1}{3}$ and $J = \intoo{1}{5}$ . Draw both on the same line: they overlap between $1$ and $3$ . Therefore

I \cap J = \intoc{1}{3}, \qquad I \cup J = \intco{-1}{5}.

Note the brackets: $1 \notin J$ so $1 \notin I \cap J$ , but $3 \in I$ and $3 \in J$ , so $3 \in I \cap J$ .

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