Tautomerism is a form of isomerism where compounds, called tautomers, interconvert by relocating a proton and a double bond. This dynamic equilibrium commonly involves keto-enol tautomers, where a ketone form shifts to an enol form. For example, in acetoacetic acid, the keto form (with a C=O bond) ...
SETS RELATIONS AND FUNCTION
SETS
A set is a collection of well defined and well distinguish objects of our
perception or thought.
1. NOTATION
Sets, in mathematics, are an organized collection of objects and can be
represented in set-builder form or roster form. Usually, sets are represented in
curly braces {}, for example, A = {1,2,3,4} is a set.
2. REPRESENTATION OF SET
The sets are represented in curly braces, {}. For example, {2,3,4} or {a,b,c}
or {Bat, Ball, Wickets}. The elements in the sets are depicted in either
the Statement form, Roster Form or Set Builder ForThe sets are represented
in curly braces, {}. For example, {2,3,4} or {a,b,c} or {Bat, Ball, Wickets}. The
elements in the sets are depicted in either the Statement form, Roster Form
or Set Builder Form.
Statement Form
In statement form, the well-defined descriptions of a member of a set are
written and enclosed in the curly brackets.
For example, the set of even numbers less than 15.
In statement form, it can be written as {even numbers less than 15}.
Roster Form
In Roster form, all the elements of a set are listed.
For example, the set of natural numbers less than 5.
Natural Number = 1, 2, 3, 4, 5, 6, 7, 8,……….
, Natural Number less than 5 = 1, 2, 3, 4
Therefore, the set is N = { 1, 2, 3, 4 }
Set Builder Form
The general form is, A = { x : property }
Example: Write the following sets in set builder form: A={2, 4, 6, 8}
Solution:
2=2x1
4=2x2
6=2x3
8=2x4
So, the set builder form is A = {x: x=2n, n ∈ N and 1 ≤ n ≤ 4}
Also, Venn Diagrams are the simple and best way for visualized
representation of sets.
3.Types of Sets
We have several types of sets in Maths. They are empty set, finite and
infinite sets, proper set, equal sets, etc. Let us go through the classification
of sets here.
Empty Set
A set which does not contain any element is called an empty set or void
set or null set. It is denoted by { } or Ø.
A set of apples in the basket of grapes is an example of an empty set
because in a grapes basket there are no apples present.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ayushmishra3. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $11.19. You're not tied to anything after your purchase.
