Statistics How To

A Union B (Union Set)

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What is “A Union B”?

A Union B means that A happens or B happens (or perhaps both happens). These could be events, objects, or just about anything else. For example:
A person buys a scratch off lottery ticket. Event A could be “wins up to $10” and event B could be “wins $10 or more”. The possibility of winning anything at all (i.e. the set of all possibilities) is called the union.
An asteroid on its way to Earth might hit the Earth (A) or miss it (B). The set of possibilities “hit” or “miss” is the union.
A box of chocolates might be milk (A), dark (B) or both. The union is {milk, dark, both}.

How to Represent A Union B Mathematically

Unions are represented mathematically by a cup symbol (∪). Let’s say you wanted to represent whether a list of “black objects” OR “white objects” can be found in a gift shop. The list contains Shells, Dog Figurines, Ceramics, Hats, Jewelry, Paintings, Face Cream and Dresses. You would write the union as:
Black ∪ White = {Shells, Dog Figurines, Ceramics, Hats, Jewelry, Paintings, Face Cream, Dresses, Coal, Snow}.
All of the listed items are, together, a union: any particular object could be black, white, or perhaps could be both at the same time (a figurine of a Dalmatian for example would be both black and white).

You can represent A Union B with a Venn diagram. For example, this Venn diagram shows A Union B of household objects divided into two categories: A (electronic) and B (non-electronic).

a union b

A Venn diagram showing household objects that could be classified as either electronic or non-electronic.

You may notice that there’s some overlap on the diagram. Toothbrushes and lawnmowers can be electronic (or manual). This overlap is called an intersection.

Stephanie Glen. "A Union B (Union Set)" From Elementary Statistics for the rest of us!

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