Question

S = {a, b, c, d, e}
How many proper subsets does the set S have?

Answer 1

Answer:

Find all sets with only 1 element; {a}, {b}, ...

Find all sets with only 2 elements; {a,b}, {a,c}, ...

Find all sets with only 3 elements; {b,c,d}, ...

Find all sets with only 4 elements; {a,b,c,d}, ...

Don't forget the null set or empty set, the set containing no elements, denoted by the symbol Ø. The null set is a subset of every set.

Don't forget the set containing all of the elements; every set is a subset of itself.

All sets are proper subsets except the set that contains all of the elements.

The number of subsets is always 2^n where n is the number of elements in the set; in this case 5.

There should be 2^5=32 subsets including the empty set and the set itself.

Step-by-step explanation:

Answer 2

Given :  Set S = {a, b, c, d, e}

To Find :  How many proper subsets does the set S have

Solution:

S = {a, b, c, d, e}

There are 5 elements

n(S) = 5

A set containing x elements  have subsets  = 2ˣ

There are 5 elements hence x = 5

Number of subsets = 2⁵  = 32

proper subsets  are the subset other than the subset having all the elements

Hence proper subsets = 2ˣ - 1

= 2⁵  - 1

= 32 - 1

= 31

There are 31  proper subsets.

The set S has 31 proper subsets

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