036. Unions, Intersections and Venn Diagrams

The Intersection of A and B, written A∩B and read as “A intersection B”, consists of those elements that are in common to Both A and B. Given A∩B, the events A and B are called Joint events. The probability that two or more events will all occur is called Joint probability.

A Venn diagram is a useful tool to portray the relationship between sets. It was developed by an English mathematician John Venn (1834-1923). It’s shown in Figure 4.1.

Figure 4.1 – Venn Diagram

The Union of A and B, written AUB and read as “A union B”, consists of those elements that are in either A or B or both.

Example 4.3. Given a deck of 52 cards, set A is all hearts and set B is all kings. Identify A∩B and AUB.

Solution. The two sets are shown in the Venn diagram. See Figure 4.2.

Figure 4.2 – A Venn Diagram for Deck of Cards

AUB is the set of all cards that are in either set A or set B, and consists of all hearts (including the king) and all kings (including the heart).

A∩B contains only those elements that are in both A and B, i. e. those elements that are both hearts and kings.

Interpretation. The event AUB is satisfied if Either a king or a heart is drawn from the deck. The joint event A∩B Is satisfied Only If The king of hearts is drawn.

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