Question

Determine the number of subsets for the following sets:
1.{ } or
2. { 1}
3. { 1, 2, 3 }
4. { 1, 2, 3, 4 }
5. A set of 5 elements or members
6. A set of 6 elements

Answer 1

1. 1

2. 2

3. 7

4. 17

5. 26

6. 37

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Answer 2

Answer:

Step-by-step explanation:

Now here,

For any subset

subset = $2^N-1$

N = given set.

1. { } subset is  

= from the above set, the subset is zero, because it contains an empty value therefore it is also called an empty Set.

2. { 1 } subset is

= From the above set, the subset is two, because it contains one and an empty subset therefore it is called a single subset event.

3. { 1, 2, 3 }  subset is

= From the above set, the subset contains:

{ {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} and {} }

Where, {} is an empty set, therefore 8 is the subset of set { 1, 2, 3 }.

4. { 1, 2, 3, 4 } subset is

= From the above set, the subset contains:

{ {1},{2},{3},{4},{1,2},{2,3},{3,4},{4,1},{1,3},{2,4},{1,2,3},{2,3,4},{3,4,1},{4,1,2},{1,2,3,4},{} }

Therefore 16 is the subset of set { 1, 2, 3, 4 }.

5. A set of 5 elements or members

= From the above set, the subset contains:

Let's assume that, the set of 5 elements is {a, b, c, d, e}

{ {a}, {b}, {c}, {d}, {e}, {ab}, {ac}, {ad}, {ae}, {bc}, {bd}, {be}, {cd}, {ce}, {de},

{abc}, {abd}, {abe}, {acd}, {ace}, {ade}, {bcd}, {bce}, {bde}, {cde}, {abcd}, {abce}, {abde}, {acde}, {bcde}, {abcde} }

Therefore 32 is the subset of the set of 5 elements or members.

6. A set of 6 elements

= From the above set, the subset contains:

Let's assume that, the set of 6 elements is {a, b, c, d, e, f}

{ (a),(b),(c),(d),(e),(f),(a,b),(a,c),(a,d),(a,e),(a,f),(b,c),(b,d),(b,e),(b,f),(c,d),(c,e),(c,f),(d,e),(d,f),(e,f),(a,b,c),(a,b,d),(a,b,e)(a,b,f),(a,c,d),(a,c,e),(a,c,f),(a,d,e),(a,d,f),(b,c,e),(b,c,f),(b,c,d),(b,d,e),(b,d,e),(c,d,e),(c,d,f),(b,c,d,e),(b,c,d,f),(a,c,d,e),(a,c,d,f),(a,b,d,e),(a,b,c,e),(a,b,c,d), }

Therefore 64 is the subset of the set of 6 elements or members.

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