Bio/statistics Handout on basic set terminology

1) Set terminology

My purpose in this handout is to supply you with a dictionary of sorts to translation some of the commonly used symbols for sets of elements. In what follows, capital letters designate sets and lower case letters designate elements.

· A Ì B “A is a subset of B”.

· A Ç B “The set of elements that are in both A and B”. Thus AÇB Ì A and also

AÇB Ì B. The set AÇB is called the “intersection between A and B”.

· A È B “The set of elements that are in either A or B”. Thus, A Ì AÈB and also

B Ì AÈB. This set is called the “union of A and B”.

· A = B This means that A and B have the same elements so are identical.

· ø This is the symbol for the “empty set”, the set with no elements. Thus,

AÇB = ø when A and B have no points in common.

· a Î A This means that the a is an element of the set A.

· a Ï A This means that a is not an element of the set A.

· A^c This means the set of elements that are not in the set A.

· {···} Brackets are typically used to enclose the list of elements of a set. For

example, {1, 2, 3} signfies the set of whole numbers whose elements are 1, 2, and 3.

· If a set of N numbers or variables or unknowns is labeled by the consecutive integers as in {a₁, . . . , a_N}, then ∑_1≤j≤N a_j is nothing more than a₁ + a₂ + · · · + a_N.