1.13 Summary

NCERT Class 11 Mathematics Textbook for blind and visually impaired students made screen readable by Professor T K Bansal.'

This chapter deals with some basic definitions and operations involving sets. These are summarised below:

• A set is a well-defined collection of objects.

• A set which does not contain any element is called empty set.

• A set which consists of a definite number of elements is called a finite set, otherwise, the set is called infinite set.

• Two sets A and B are said to be equal if they have exactly the same elements.

• A set A is said to be subset of a set B, if every element of A is also an element of B.

• Intervals are subsets of R.

• A power set of a set A is collection of all subsets of A. It is denoted by P(A).

• The union of two sets A and B is the set of all those elements which are either in A or in B.

• The intersection of two sets A and B is the set of all elements which are common both to sets A and B.

• The difference of two sets A and B in this order is the set of elements which belong to A but not to B.

• The complement of a subset A of universal set U is the set of all elements of U which are not the elements of A.

• For any two sets A and B,


(A ∪ B)′ = A′∩ B′ and


( A ∩ B )′ = A′ ∪ B′

• If A and B are finite sets such that A ∩ B = φ, then


n(A ∪ B) = n (A) + n (B).

• if, A ∩ B ≠ φ, then


n(A ∪ B) = n (A) + n (B) − n (A ∩ B)