How many subsets does set A have?

  • Thread starter lipun4u
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In summary, the number of subsets of set A, where A={1,2,3}, is 8 and the number of proper subsets is 7. This can be calculated using the formula 2^(n), where n is the number of elements in A.
  • #1
lipun4u
7
0
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
 
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  • #2
lipun4u said:
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

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
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
the formula for the cardinality of the powerset is 2^(cardinality of the set) hence the number is 8 not 7
 
  • #5
i m saying ab proper subset not subset...
 
  • #6
lipun4u said:
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 ??

Yes, that's correct.
 
  • #7
ice109 said:
the formula for the cardinality of the powerset is 2^(cardinality of the set) hence the number is 8 not 7

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.)
 

1. What is the difference between a subset and a proper subset?

A subset is a set that contains all the elements of another set, while a proper subset is a subset that contains some, but not all, of the elements of another set.

2. How can you determine if one set is a subset of another set?

To determine if one set is a subset of another set, you can check if all the elements of the first set are also present in the second set.

3. Is the empty set considered a subset or a proper subset?

The empty set is considered a subset of every set, but not a proper subset of any set.

4. How many proper subsets can a set have?

A set can have an infinite number of proper subsets, as long as it has at least two elements.

5. Can a set be its own proper subset?

No, a set cannot be its own proper subset because a proper subset must have at least one element that is not present in the original set.

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