Question

What are the various ways in which we can write sets?

Answer 1

Answer:

In this question,

The empty set can be written ∅.

 {} also denotes an empty set.

For infinite or large sets, another notations must be used. Common ones are N and Z to denote the infinity of natural numbers and integers, respectively. Subsets of these sets can be “generated” using a combination of curly braces and the mid bar. For example, {n²∣n∈N} can be used to denote the infinite set of perfect squares.

Multidimensional sets can be written using similar notations, e.g.{(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)} denotes the set of combinations of values 1 to 3. It can also be “generated”, e.g. {(i,j)∣(i,j)∈{1,2,3}²∧i<j}. Note the “²” symbol to denote the cartesian product of a set with itself.

Answer 2

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SET : A set is a well defined collection of distinct objects

Example :

• S = { 1,2,3,4,........}
• The of Real numbers

REPRESENTATION OF SETS

There are three ways in which we can represent a set

The ways are :

(i) Statement form

(ii) Roster or tabular form

(iii) Set builder form

(i) Statement form

In this form a set is written in statement form

Example

• The set of whole numbers less than 9
• The natural numbers between 1 and 5

(ii) Roster or tabular form

In this form a set is written in tabular form

Example

• S = { 1,2,3,4,........}
• The set of whole numbers W = { 0,1,2,3,....}

(iii) Set builder form

In this form a set is written in set builder form

Example

$\sf{S = \{ \: x \in \mathbb{N} : 1 < x < 11 \: \} }$

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LEARN MORE FROM BRAINLY

Represent all possible one-one functions from the set A = {1, 2} to the set B = {3,4,5) using arrow diagram.

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