Question

A= {x:x is a multiple of 3, x is greater than or equal to 3 and smaller than or equal to 12} in roster form

Answer 1

$\bigstar\large \red{ \pmb{ \bf Required \: Answer }} \bigstar$

• Given that X is a multiple of 3 such that it is ≥ 3 and ≤ 12.
• such multiples of 3 are :-
• 3,6,9,12

$\: \: \: \: \: \: \: \: \therefore \underline{ \frak{ the \: roaster \: form \: of \: this \: set \: is : - }}$

$: \implies \boxed{ \pink{{\sf A = {\{ 3,6,9,12} \}}}} \bigstar$

ADDITIONAL INFORMATION:-

• Empty set is a subset of every set
• Every set is a subset of itself
• improper subsets are always equal sets and vice versa
• No of subsets = 2^{no. of elements in that set}
• Power if set a set formed by all the subsets of that set.

Answer 2

Given :-

A= {x:x is a multiple of 3, x is greater than or equal to 3 and smaller than or equal to 12}.

To Find :-

The roster form of the given set .

Used Concepts :-

• In roster we have to find all the elements of a finite set and write them inside braces .

Solution :-

Let's start with the given that x is a multiple of 3 , x is greater than or equal to 3 and smaller than or equal to 12 .

If we have to find first three multiples of x then , Then it's multiple are x , 2x , 3x . In Easy language , The table of the given number .

Let , find the multiples of 3 , such that they are greater than or equal to 3 and less than or equal to 12 . They are as follows :-

3 , 6 , 9 , 12 .

Here , all conditions apply on the above elements of this question .

Hence , A = { 3 , 6 , 9 , 12 } .

Additional Information :-

For a set " A " .

• The empty / void / null set is subset of every set ( Including itself ) .
• The empty set is proper subset of every set ( Except Itself ) .
• If n ( A ) = m , them no. of subsets of A = 2^m .
• If n ( A ) = m , then no. of proper subsets of A = 2^m - 1 .
• If a subset of A is not proper , then it is improper subset .
• Let , Another set B , Then A is called the proper subset of B if and only all members of A are also members of B , but there is at least one element in B , that didn't belongs to A .
• Sets are always written in braces while ordered pairs in parentheses .
• The power set of A is the Set of all subsets of A .
• If n ( A ) = m ,then n { ( P ( A ) } = 2^m .
• Every set is subset of itself But not proper , because If no . of subsets of A are 2^m , then we have to minus 1 from the no. of subsets because A is not proper subset of A , then the formulae to find no. of proper subsets is 2^m - 1 , where n ( A ) = m .
• If n ( A ) = m , then total no. of unordered pairs of disjoint ( not overlapping ) subsets of A are 3^m- 1 /2! + 1.