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What Is Union and Intersection of Sets?

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Sets are central in probability theory. When considering probabilities within the context of set theory, it becomes easier to structure exercises and solve problems.

Theory

Union

“ $A$ union $B$ ” is all the elements in $A$ , $B$ , or both. Mathematically, this is written as follows:

A \cup B

You read $\cup$ as “or”.

In other words, $A \cup B$ is a new, compound set consisting of all the outcomes unique to $A$ , all outcomes unique to $B$ , as well as all the outcomes that $A$ and $B$ have in common. You can visualize it with this Venn diagram:

Venn diagram for all outcomes unique to A and B

Example 1

Let $A$ be the set ${1, 3, 5}$ and $B$ be the set ${3, 5, 6}$ . The union $A \cup B$ is the set of outcomes ${1, 3, 5, 6}$ .

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Theory