Question

1.What must be used to tell if a collection of items is a set?

Answer 1

1. A set is described either by listing all its elements between braces { } (the listing method), or by enclosing a rule within braces that determines the elements of the set (the rule method).
Example: So if P(x) is a statement about x, then S = { x | P ( x )} means “S is the set of all x such that P(x) is true.”

2. Types of set:
• Empty, or null, set {∅}.
• finite sets
• infinite set.

3. An infinite set: The set whose elements cannot be listed, i.e., set containing never-ending elements. Example: Set of all points in a plane.

4. The union of two given sets is the smallest set which contains all the elements of both the sets. To find the union of two given sets A and B is a set which consists of all the elements of A and all the elements of B such that no element is repeated. The symbol for denoting union of sets is ‘∪’.

The union of sets A and B, denoted by A ∪ B, is the set of elements formed by combining all the elements of A and all the elements of B into one set.