Pls give me the notes of ncert class 11 mathematics chapter 1 Sets!! Pls help me guys, soon.............. The best answer will be marked as "Brainliest"!!!
Answers
Types of sets:
Empty set: A set which does not contain any element is called empty set or null set or void set. It is denoted by or { }.
Singleton set: A set, consisting of a single element, is called a singleton set.
Finite set: A set which consists of a definite number of elements is called finite set.
Infinite set: A set, which is not finite, is called infinite set.
Equivalent sets: Two finite sets A and B are equivalent, if their cardinal numbers are same, .i.e, .
Equal sets: Two sets A and B are said to be equal if they have exactly the same elements.
Subset: 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.
Proper set: If A B and A B, then A is called a proper set of B, written as A B.
Universal set: If all the sets under consideration are subsets of a large set U, then U is known as a universal set. And it is denoted by rectangle in Venn-Diagram.
Power set: A power set of a set A is collection of all subsets of A. It is denoted by P(A).
Venn-Diagram: A gepmetrical figure illustrating universal set, subsets and their operations is known as Venn-Diagram.
Union of sets: The union of two sets A and B is the set of all those elements which are either in A or in B.
Intersection of sets: The intersection of two sets A and B is the set of all elements which are common. The difference of two sets A and B in this order is the set of elements which belong to A but not to B.
Disjoint sets: Two sets A and B are said to be disjoint, if .
Difference of sets: Difference of two sets i.e., set (A – B) is the set of those elements of A which do not belong to B.
Compliment of a set: 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. A’ = U – 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)
✴Any well defined collection of objects is called a set.
✴The objects which belong to the set are called its members or elements.
✴The sets are usually denoted by capital letters A,B,C etc.. , and the members of the set are denoted by small letters.
Sets can be represented in 3 ways
✴Description method
✴Tabular form
✴Set builder form
Remarks -
- the order of listing the elements in a set can be changed
- if one or more elements of a set are repeated , the set remains the same
- each element of the set is listed once and only once repetitions are removed
- If the number of elements in a set is very large , then we can represent the set by writing a few members which clearly indicates the structure of the elements of the elements of the set followed by '...' and then write the last number if it exists