- A well-defined collection of definite objects is called a set.
- In roster method of representing a set, all the elements are listed in the set.
- In property method of representing a set, all the elements are represented by stating all the properties which are satisfied by the elements of the set and not by any other element.
- A set is said to be a
- infinite set if it contains infinitely many elements.
- null set if it does not contain any element.- singleton set if it contains only one element.
- Two sets are said to be
- Equivalent sets if the elements of one set can be put in one-one correspondence with the elements of the other set.
- Equal sets if every element of one set is in the other set and vice-versa- A set A is said to be a subset of set B if every element of A is an element of B. If A is subset of B, then it is expressed as A Í B.
- A set A is said to be a proper subset of set B if A is a subset of B and A is not equal to B. If A is a proper subset of B, then we write A Ì B.
In order to show that A Ì B it is sufficient to show that each element of A is in B and there is at least one
element in B, which is not in A.
- Set Operations
- Important results
- If A is a subset of universal set X, then complement of A is defined as the set of all those elements of X which are not in A and it denoted by A' or by Ac. We have A' = X - A.
- De Morgan's laws
- Let A, B be finite sets. Then
- Let A,B,C be finite sets.
