# Subset and proper subset

1. Jun 20, 2008

### lipun4u

Let 's Consider a set A where A={1,2,3}

Can anyone tell me
1>no of subsets of A
2>no of proper subsets of A

Regards,
Asit

2. Jun 20, 2008

### Hubert

What have you tried already? If you know the definition of subset, it should be easy enough to make a list of all the subsets and then count them. There is also a very simple formula relating the number of subsets of a given set to its cardinality.

After you answer part 1, part 2 is simply the number of subsets of A minus the number of those sets which are not proper subsets. (what is the definition of proper subset?)

3. Jun 20, 2008

### lipun4u

i know the asnwer

if A has three elements, proper subset of A will be 7
becoz all the subsets will be Null,{1},{2},{3},{1,2},{2,3},{1,3}
subsets of A will be 8 BY INCLUDING {1,2,3}

I asked it, becoz i m not sure ab it.

Am i correct ab it ??

4. Jun 20, 2008

### ice109

the formula for the cardinality of the powerset is 2^(cardinality of the set) hence the number is 8 not 7

5. Jun 21, 2008

### lipun4u

i m saying ab proper subset not subset....

6. Jun 21, 2008

### Hubert

Yes, that's correct.

7. Jun 22, 2008

### HallsofIvy

If a set, A, contains n members, then it has 2n subsets. Since that includes A itself, which is not a proper subset of itself, A has 2n-1 proper subsets. (And A has 2n-2 proper, nonempty subsets.)