Question

class 11 maths lab manual activity 1 solution​

Answer 1

Class 11th lab manual Activity-1

Given: Subsets of a  given set.

To find: To find the number of subsets of a

given set and verify that if a set has n

number of elements, then the total

number of subsets is 2n

Solution:

1.  $A_{0}$ be empty set ∅

           ∅ ≤ ∅

    No. of subsets of   $A_{0}$ = 1 = $2^{0}$

2. $A_{1}$ is a set that has one element $a_{1}$

   Subsets of $A_{1}$ are {$a_{1}$}, ∅

    No. of subsets of $A_{1}$ = $2^{1}$

3. $A_{2}$ = {$a_{1}$ , $a_{2}$ }

   Subsets of $A_{2}$ are ∅ , {$a_{1}$} ,{ $a_{2}$} ,{$a_{1} , a_{2}$}

No. of sunsets of $A_{2}$ = 4 = 2

4.$A_{3}$ = {$a_{1} ,a_{2} , a_{3}$}

  Subsets of $A_{3}$ = ∅ {$a_{1}$} ,{ $a_{2}$} ,{ $a_{3}$} ,{$a_{1} , a_{2}$}, {$a_{2} , a_{3}$}, {$a_{3} , a_{1}$}

                              {$a_{1}, a_{2} , a_{3}$}

  No.of subsets of $A_{3}$ = 8= 2³

Therefore the observations of the activity are :

• No. of subsets of $A_{0}$ = $2^{0}$ =1

• No. of subsets of $A_{1}$ = $2^{1}$ =2

• No. of subsets of $A_{2}$ = $2^{2}$ = 4
• No.of subsets of $A_{3}$ = $2^{3}$ = 8

Similarly,

No. of elements$A_{10}$ =$2_{10}$

$A_{10} = 2^{10}$

Continuing this way, no. of subsets A which is having n elements is $2^{n}$

No.of subsets of $A_{n} = 2^{n}$