JEE Exam > JEE Videos > Sets and Functions > Identify Sets (Part-3 ) - Solution
Identify Sets (Part-3 ) - Solution Video Lecture | Sets and Functions - JEE
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FAQs on Identify Sets (Part-3 ) - Solution Video Lecture - Sets and Functions - JEE
| 1. What is the importance of sets in mathematics? |  |
Ans. Sets are fundamental concepts in mathematics that help in organizing and categorizing objects or elements. They provide a way to study the relationships and properties of these elements. Sets are widely used in various branches of mathematics, such as algebra, calculus, and probability theory.
| 2. How are sets represented or described? | |
Ans. Sets can be represented or described in different ways. One common way is by listing the elements within curly braces, separated by commas. For example, {1, 2, 3} represents a set with three elements. Another way is by using set-builder notation, where a condition or rule is given to define the set. For instance, {x | x is an even number} represents the set of all even numbers.
| 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 the symbol "n(A)" or "card(A)", where A represents the set. For example, if A = {1, 2, 3}, then n(A) = 3 since the set has three elements. In some cases, the cardinality of a set can be infinite, such as the set of all natural numbers.
| 4. Can sets have overlapping elements? | |
Ans. Yes, sets can have overlapping elements. When two or more sets share common elements, it is called an overlapping or intersecting set. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A and B have overlapping elements {2, 3}. It is important to note that the overlapping elements are counted only once when determining the cardinality of the sets.
| 5. How are sets related to Venn diagrams? | |
Ans. Venn diagrams are graphical representations used to visualize the relationships between sets. In a Venn diagram, sets are represented by circles or ovals, where each circle represents a set. The overlapping regions between the circles show the common elements shared by the sets. Venn diagrams are a helpful tool in understanding set operations, such as union, intersection, and complement.
Text Transcript from Video
let's discuss the solution 5 odd natural
numbers there are infinite out natural
numbers it is not defined which 5 odd
natural numbers should be the part of
this collection since the members are
not well defined this collection is not
a set
five odd natural numbers divisible by
three as in the previous case there are
infinite odd natural numbers divisible
by three again it does not define which
five should be the part of this
collection since the members are not
well defined this collection is not a
set
all laud natural numbers divisible by
three and less than ten this collection
includes all the odd natural numbers
divisible by three and less than ten
which are three and nine since the
members are well defined this collection
is a set
numbers there are infinite out natural
numbers it is not defined which 5 odd
natural numbers should be the part of
this collection since the members are
not well defined this collection is not
a set
five odd natural numbers divisible by
three as in the previous case there are
infinite odd natural numbers divisible
by three again it does not define which
five should be the part of this
collection since the members are not
well defined this collection is not a
set
all laud natural numbers divisible by
three and less than ten this collection
includes all the odd natural numbers
divisible by three and less than ten
which are three and nine since the
members are well defined this collection
is a set
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Dec 25, 2024 Last updated |
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