Which one is different from the others ?
(i) empty (ii) void (iii) zero (iv) null :
- (i)
- (ii)
- (iii)
- (iv)
The Correct Option is C
Approach Solution - 1
Approach Solution -2
Ans. Set Theory, in Mathematics, is a branch of mathematics that helps us understand a collection of objects, usually called, sets. These well-defined objects are also known as elements and could be of any kind and in any form.
- These may be alphabets, numbers, lines, shapes or even variables.
- For example, since the number of players found in a cricket team can only be 11 at one time, thus it is a finite set.
- Georg Cantor (1845-1918), a German mathematician, first gave the concept of the ‘Theory of sets’ or ‘Set Theory’.
- An element ‘a’ which belongs to a set A can also be represented as a ∈ A’, ‘a ∉ A’ denotes that a is not an element of the set A.
Sets can be represented in a variety of methods, such as:
- Statement Form
- Roaster Form or Tabular Form Method
- Set Builder Method
Null Set or Empty Set
A set with absolutely no elements inside it is called an empty set or null set. The cardinality or count of elements of this set is 0. For example, name a month which consists of only two Mondays. We know that it is not possible, because Monday comes at least 4 times in a month.
Hence, it is represented as set A = {...}. It is denoted by the symbol Φ and is to be read as ‘phi’.
It is sometimes also known as a void set.
Top Questions on Sets
- The distance of the point \( (2, 3) \) from the line \( 2x - 3y + 28 = 0 \), measured parallel to the line \( \sqrt{3}x - y + 1 = 0 \), is equal to
- Two finite sets have $ m $ and $ n $ number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $ m $ and $ n $ are respectively.
The shaded region in the Venn diagram represents
- Which of the following is a null set?
- Which of the following statement is true?
Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".