Set Operations

*The union of two events E and F, denoted by E ∪ F, is defined as

the set of outcomes that are either in A or in B, or both.

The event E ∪ F occurs if either E, or F, or both E and F occur.

*The intersection of two events E and F, denoted by E ∩ F,

is defined as the set of outcomes that are common to E and F. 

*The complement of an event E, denoted by E' or 

is defined as the set of all outcomes not in E. The event E'

occurs when the event E does not occur and vice versa.

A deck of playing contains 52 cards. We perform the experiment of

randomly selecting one card from the deck.

S = The collection of all 52 cards

Let us consider the following 4 events

A = The card selected is the king of hearts

B = The card selected is a king

C = The card selected is a heart

D = The card selected is a face card

How many outcomes comprising each of these four events?

A:

B: 

C:

D:

Determine D', B ∩ C, B ∪ C, C ∩ D 

The operations of forming unions, intersections, and complements of 

events obey certain rules similar to the rules of algebra. We list a few of these rules:

Commutative laws E ∪ F = F ∪ E         E F = F E ( OR E ∩ F = F ∩ E) 

Associative laws (E ∪ F) ∪ G = E ∪ (F ∪ G)         (E F) G = E (F G)

Distributive laws (E ∪ F) ∩ G = (E ∩ G) ∪ (F ∩ G) 

(E ∩ F) ∪ G = (E ∪ G) ∩ (F ∪ G)

The following useful relationships between the three basic operations

of forming unions, intersections, and complements are known as DeMorgan’s laws: