NCERT Class 11 Mathematics/Sets – Chapter 1
NCERT Class 11 Mathematics/Sets – Chapter 1 is about the important points to be studied about Sets. Here you can find out the important definitions of sets and different types of sets.
NCERT Class 11 Mathematics/SETS – Chapter 1
Important Points to Remember:
Set: A set is a well-defined collection of objects.
There are two methods of representing a set:
i) Roster or tabular form
ii) Set-builder form
In roster form, the order in which the elements are listed is immaterial.
While writing the set in roster form an element is not generally repeated.
The Empty Set or the Null Set or the Void Set:
A set which does not contain any element is called the empty set or the null set or the void set.
Finite and Infinite Sets:
A set which is empty or consists of a definite number of elements is called finite otherwise, the set is called infinite.
Equal Sets: Two sets A and B are said to be equal if they have exactly the same elements and we write A=B.
Otherwise, the sets are said to be unequal.
A set does not change if one or more elements of the set are repeated.
Subsets: A set A is said to be a subset of a set B if every element of A is also an element of B.
Power set: The collection of all subsets of a set A is called the power set of A. It is denoted by P (A).
Union of sets:
The union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both).
Intersection of sets:
The intersection of two sets A and B is the set of all those elements which belong to both A and B.
Difference of sets:
The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B.
Complement of a set:
Let U be the universal set and A a subset of U. Then the complement of A is the set of all elements of U which are not the elements of A.