JEE Exam > JEE Videos > Sets and Functions > Identify Sets (Part-1) - Solution
Identify Sets (Part-1) - Solution Video Lecture | Sets and Functions - JEE
FAQs on Identify Sets (Part-1) - Solution Video Lecture - Sets and Functions - JEE
| 1. What is the significance of sets in mathematics? |  |
Ans. Sets are an essential concept in mathematics that allows us to group objects or elements together based on common characteristics. They help in organizing and categorizing data, solving problems, and forming the foundation of various mathematical theories.
| 2. How are sets represented and written in mathematical notation? | |
Ans. In mathematical notation, sets are represented by listing their elements inside curly braces {}. For example, a set containing the numbers 1, 2, and 3 can be written as {1, 2, 3}. Additionally, we can use set-builder notation to define a set based on a certain condition or rule.
| 3. What is the cardinality of a set? | |
Ans. The cardinality of a set refers to the number of elements it contains. It is denoted by |A|, where A is the set. For example, if a set A has 5 elements, then its cardinality is represented as |A| = 5.
| 4. How do we determine if two sets are equal? | |
Ans. Two sets are considered equal if they have exactly the same elements. In other words, if every element of set A is also an element of set B, and vice versa, then we can say that A equals B. This can be expressed as A = B.
| 5. What is the power set of a set? | |
Ans. The power set of a set is the set that contains all possible subsets of the original set. It includes the empty set and the set itself. For example, if we have a set A = {1, 2}, then its power set is P(A) = { {}, {1}, {2}, {1, 2} }. The power set has a total of 2^n subsets, where n is the number of elements in the original set.
Text Transcript from Video
let's discuss the solution to check if
the given collection is a set we just
need to see whether the members of the
collection are well defined or not if
the members of a collection are well
defined then it is a set collection of
all the months of a year the members of
this collection are the names of the 12
months clearly this collection is
well-defined and hence it is a set
collection of most dangerous animals of
the world the criterion for determining
an animal as dangerous will vary from
person to person so the members of this
collection are not well-defined and
hence it is not a set
collection of all the rivers of the
world this collection includes the names
of all the rivers of the world the
members of this collection are well
defined and hence it is a set
the given collection is a set we just
need to see whether the members of the
collection are well defined or not if
the members of a collection are well
defined then it is a set collection of
all the months of a year the members of
this collection are the names of the 12
months clearly this collection is
well-defined and hence it is a set
collection of most dangerous animals of
the world the criterion for determining
an animal as dangerous will vary from
person to person so the members of this
collection are not well-defined and
hence it is not a set
collection of all the rivers of the
world this collection includes the names
of all the rivers of the world the
members of this collection are well
defined and hence it is a set
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