SOLUTION: The number of subsets of a set with n elements is n^2 True or False?

Question 994749: The number of subsets of a set with n elements is n^2
True or False?

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

False it's 2ⁿ.

That's because when constructing a subset of a given set,

There are 2 possible choices to make for the 1st element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2 choices for the first element of the given set in
taking a subset.
---
There are 2 possible choices to make for the 2nd element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2*2 or 2² choices for the first 2 elements 
of the given set in taking a subset from it.
---
There are 2 possible choices to make for the 3rd element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2*2*2 or 2³ choices for the first 3 elements 
of the given set in taking a subset from it.
---
...
...
...
There are 2 possible choices to make for the nth element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2*2*...*2 or 2ⁿ choices for the n element 
of the given set in taking a subset from it.

Edwin

RELATED QUESTIONS
A finite set (Omega) has n elements. Show that if we count the empty set and (Omega) as... (answered by stanbon)

37. In this exercise we study the connection between sets (from Chapter 7) and... (answered by stanbon)

Is it true or false if the set A has three elements,then P(P(A)) )the power of the power... (answered by solver91311)

Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets... (answered by KMST)

A and B are subsets of universal set U. If n(U)=28, n(A)=11, n(B′)=19, and... (answered by solver91311)

A set U is partitioned into two subsets, G and H. The number of elements in H is four... (answered by Fombitz,MathLover1)

Find the number of subsets of a set with 5... (answered by Fombitz)

36. If the number of subsets with 4 elements of a set A is equal to the number of... (answered by Edwin McCravy)

if the number of subsets with 4 elements of a set A is equal to the number of subsets... (answered by KMST)