Scribd
Upload
59 views2 pages

Activity: Bjective

The document outlines an activity to demonstrate that the number of subsets of a set with n elements is 2^n. It provides a step-by-step method for constructing sets with increasing elements and calculating their subsets. The activity concludes with observations and applications for calculating subsets.

Uploaded by

rishi.barchha
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
59 views2 pages

Activity: Bjective

The document outlines an activity to demonstrate that the number of subsets of a set with n elements is 2^n. It provides a step-by-step method for constructing sets with increasing elements and calculating their subsets. The activity concludes with observations and applications for calculating subsets.

Uploaded by

rishi.barchha
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

Activity 3

OBJECTIVE
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.
METHOD OF CONSTRUCTION

1. Take the empty set (say) A0 which has no element.


2. Take a set (say) A1 which has one element (say) a1.
3. Take a set (say) A2 which has two elements (say) a1 and a2.
4. Take a set (say) A3 which has three elements (say) a1, a2 and a3.

DEMONSTRATION
1. Represent A0 as in Fig. 1.1

Here the possible subsets of A0 is A0 itself


only, represented symbolically by φ. The
number of subsets of A0 is 1 = 20 .
2. Represent A1 as in Fig. 1.2. Here the subsets
of A1 are φ, {a1}. The number of subsets of
A1 is 2 = 21
3. Represent A2 as in Fig. 1.3

Here the subsets of A2 are φ, {a1}, {a2},


{a1, a 2}. The number of subsets of
A2 is 4 = 22.
4. Represent A3 as in Fig. 1.4
Here the subsets of A3 are φ, {a1},
{a2}, {a3),{a1, a2}, {a2, a3) ,{a3, a1)
and {a 1 , a 2 , a 3}. The number of
subsets of A3 is 8 = 23.
5. Continuing this way, the number of
subsets of set A containing n
elements a1, a2, ..., an is 2n.

OBSERVATION
1. The number of subsets of A0 is __________ = 2
2. The number of subsets of A1 is __________ = 2
3. The number of subsets of A2 is __________ = 2
4. The number of subsets of A3 is __________ = 2
5. The number of subsets of A10 is = 2
6. The number of subsets of An is = 2
APPLICATION
The activity can be used for calculating the number of subsets of a given set.

You might also like